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A L L E N

1

ODE F

65 = 3

-

(1) 6 5 2 3

(2) 65222

(3)

=3

(4) 6 5 2 3

C6H5

CH CH CH3+HBr

C6H5

CH CH2

CH3

Br

C6H5

CH CH2CH

3

Br

Aring

983079 025

40

300 725

300 25

-

(1) 1820 (2) 1676 (3) 1576 (4) 1736

300 725

40 = 725 25 = 700

= =acute

273 700 403352

300 760

22400 2 = 28

335 =acute28 3352

22400

=acute acute

=acute

28 3352 1001676

22400 025

AIPMT ndash 2015 TEST PAPER WITH SOLUTIONS

(HELD ON SUNDAY 03th MAY 2015)

24

11 times10 12 18 times10 10 50 times 10 13

83 times 10 17

3

24

(1) (2) (3) 24 (4)

+ -eacute ugrave eacute ugravereg = euml ucirc euml ucirc2

2

2 4 4

-+

- -

acuteeacute ugraveTHORN = =euml ucirc

eacute ugrave eacute ugraveeuml ucirc euml ucirc

12

2 24 4

11 10

=

2

4

-

(1) (2)

(3) (4)

( )

S

Cl

Cl

Cl

Cl

OH

Bithionol

OH

( )

()

()

(1)

(2)

(3)

(4)

3

3

7182019 AIPMT2015 Solutions

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A L L E N

2

AIPMT 2 15

-

(1) 2+ - +2 2 2O lt O lt O (2) + - 2+

2 2 2O lt O lt O

(3) - + 2+2 2 2O lt O lt O (4) 2+ + -

2 2 2O lt O lt O

A (MO)

- + +

-

2

2 2 2O O O

N 17 15 14

B 15 25 30

A K+ C2+

I

(1) C2+ lt A lt K+ (2) C2+ lt K+ lt A

(3) K+ lt A lt C2+ (4) A lt K+ lt C2+

I

A micro

1

C+2 lt K+ lt A

(1) vsTI K

(2) I K

(3)

I K

(4) I K

A

-

= THORN = -l l

ER E

K A K A R

l1

K

(1) 2

3CO --

3CO (2)3 NO

-2-3SO

(3) 2

3 3ClO SO- - (4) 2 2

3 3CO SO- -

- -

-

2

3 3

3 3

CO SO

N 42 42

A 983079983079

C5H10O

I 983079 I

- 983079983079 -

(1) 2- (2) 3-

(3) - (4)

PNHNH2

I + NOH

I 2

983079

P

N

N

R-

(C H O)5 10

A CH3 CH

2 C CH

2 CH

3

O

CH3

CH2

C CH2 CH

3

O

reduction

Zn-HgHCl

or NH NH OH2 2

mdash -

CH mdashCH mdashCH mdashCH mdashCH3 2 2 2 3

n-pentane

(1)2 2 2O O O- +lt lt

(2) 2 2 2O O O- +

gt lt

(3)2 2 2O O O- +lt gt

(4)2 2 2O O O- +gt gt

A (MO)

- +

-2 2 2

O O O

N 17 16 15

B 15 2 25

7182019 AIPMT2015 Solutions

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A L L E N

3

CODE F

O

(1) C

(2) C

(3) C

(4) C

O CH3LAring

CH3

O+

-

(1) A (2) A

(3) A (4) -A

NO

2

weakly acidic

reduction

NH2

aniline

NH OH

Phenyl hydroxyl amine

electrolytic

medium

strongly

acidic medium

NH2

OH

p-Aminophenol

nitrobenzene rearrangement

M 284 BM -

(A N = 28 = 22 C = 24 C = 27)

(1) 3+ (2) C2+ (3) C2+ (4) N2+

N

+2

= 3

8

() =2

Q ( )m = + 2

m = 28 BM

A

361 I

(1) 127 (2) 80

(3) 108 (4) 40

FCC = = =acute

361 127

2 141412 2

(1) H C C = C C C3

H

H H2

(2) H C C = C C C3

H

H H2

(3) H C C = C C C3

H

H H2

(4) H C C = C C C3

H

H H2

A C p

CH3

CH CH CH2

C

983079 H983079 () A2(SO4)3( 100 )

(1) K3F(CN)6 (2) A(NO3)3(3) K4F(CN)6 (4) K2SO4

H

( ) + -reg +3 2

2 4 43A SO 2A 3SO

= 5

( )[ ] ( )[ ]-+reg +4

6 64K F CN 4K F CN

=5 THORN = =5

N

(1)

(2)

(3) -

(4) 983079-983079

NO2

7182019 AIPMT2015 Solutions

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A L L E N

4

AIPMT 2 15

p-

-

H H H

CH3

CH3

H C3

H C3

H C2 H

(1) 8 (2) 12 (3) 16 (4) 4

CH3

CH3

H

CH2

H

H

CH3

CH3

H p = 4

p = 8

S 983079

-(1) C gt S gt B gt M (2) S gt C gt M gt B

(3) B gt M gt S gt C (4) M gt C gt S gt B

D M+2 M+2

MSO gt CSO gt SSO gt BSO44 4 4

SH

M

(1)2 NO- (2)

2 NO+

(3)3 NO- (4)

2 NO

NO2+ ( = 180)

2 3 2 2NO NO NO NO

bond angle

- - +lt lt lt frac34frac34frac34frac34frac34frac34frac34reg

I

reaction is 16 times 1012

-

(1)

(2)

(3)

(4)

K = 16 1012

K -

- F2+ ( = 26)

(1) - C ( = 17)

(2) - F ( = 26)(3) - N ( = 10)

(4) - M ( = 12)

F+2 = 36 ( = 6)

C = 12 22 26 22 35

= 11 - F+2

I C - C

(1)

H C3

C C

H C3

CH3

(2)

CH CH

(3)O NH C2 2

H

C CH

(4)H C3

H C3

C C

H

C Cl

CH3

CH3 CH

3

Cl C+

CH3

CH3 CH

3

t-butyl carbonium ion

ClCH

H

Cl CH

H

Aring

benzyl carbonium ion

[stable due to resonance]

C Cl

H

O2NH

2C H

Cl C

H

O2NCH

2 H

-I effect

Aring

CCH

3

CH3

H

Cl Cl

CCH

3

CH3

H

Aring

Secondary carbonium ion

[isopropyl carbonium ion]

7182019 AIPMT2015 Solutions

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A L L E N

5

CODE F

M

CH2

Aring

CH2

Aring

CH2

Aring CH2

Aring

A

-

(1) E (2) D

(3) N-C (4) F C

A

C

CH C CH 3

CH3

CH3

P C P

P

CH3

(I) (II) (III)

H I -

(1) II (2) III (3) I III (4) I

CHC

CH3

CH3

CH3

C

Ph

PhPh

CH3

H(I)

(II) (III)

O (III) H

CH CON+CH CH C3 3 2

CH3

CH3

CH COCH CH3 2 3

CH3

CH3

NC

-

(1)

(2) E

(3) G - K

(4) S

G

I

C (III)

25ordmC

(1) CC3middot4NH3 (2) CC3middot5NH3

(3) CC3middot6NH3 (4) CC3middot3NH3

( )eacute ugraveTHORN euml ucirc3 3 3 33CC 3NH C NH C

frac34frac34frac34frac34regeacute ugraveeuml ucirc3ANO

3 3 3C(NH ) C

A H2 O2 1 4 ()

(1) 4 1 (2) 16 1 (3) 2 1 (4) 1 4

= THORN = =2 2

2 2

H H

O O

1 1 2 4

4 4 32 1

(1) D CSO4 (2) F F(CO)5 F

(3) L H2

(4) R

( )[ ]+ reg0 05F 5CO F CO

N

B

(N )

(1) (40) N (41) (2) (40) H (72)

(3) (40) (73) (4) (22) (40)

D

H

(1) DG = 230 R K

(2) DGordm = 230 R K(3) DGordm = 230 R K

(4) DG = 230 R K

7182019 AIPMT2015 Solutions

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A L L E N

6

AIPMT 2 15

D = -0G 230RK

DG =0

983079983079

-

(1) 2 h (2) 2 3 h (3) 0 h (4) 6 h

O = ( )+l l h1

- l=2

= ( )+ =h h2 2 1 6

02 1

(1) M

(2) M

(3)

(4)

( ) ( )D gt D

K

()

times times gt times times THORN gt

S

-

(1) M2+ (2) K+ (3) F2+ (4) C2+

K+

G -

H C3 H C3 H C2C H 3 C H 2 C H 2

C H 3 C H 3 C H 2

( I ) ( I I ) ( I I I )

-

(1) III gt II gt I (2) II gt III gt I

(3) II gt I gt III (4) I gt II gt III

R CH CH R + H2

R CH2 CH

2 R +

(1 mole)

DH

micro1

-

H C3

C CC C

OH O

C CO O

H H2

OC H2 5

H C3

OC H2 5

(1) 16 1 -

(2) 9 2 -

(3) 9 1 -

(4) 18 2 -

H

CH

H

C

O H

C

H

C

O

O C

H

H

C

H

H

H

18 s + 2p

B

-

(1) PHB

(2) B - N

(3) N 6 6

(4) N 2- 6

N 2-N-6

(NH2 CH

2 COOH)

NH2 (CH

2)5COOH

s- p- -

(1) O4 (2) (CN)2(3) CH2(CN)2 (4) HCO3

7182019 AIPMT2015 Solutions

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A L L E N

7

CODE F

O

OO O

s = 4 p = 4

C(CN)63 -

(1) C(CN)63

-

(2) C(CN)63

(3) C(CN)63

- (4) C(CN)63

-

C(CN)6 3

C+3 = 36 40 40

Q

-

(1) DS (2) D

(3) DP = P - PR (4) DH

F DS

gt 0

-

(1) E (2) E-

(3) (4) C

G -

CH3

(I) (II) (III)

CH3CH3

CH3 CH3

CH3

OOO

(1) I III (2) II III(3) I II III (4) I II

CH3

CH3

O

H

CH3

CH3

OH

O

CH3

CH3

OH

CH3

CH3

H

O

CH3

CH3

OH

CH3

CH3

H

-

-

(1) F

(2) S

(3) M

(4)

=12

0693

K

12

A -

OHCC

CC

CH

CH3

H2

O

CH3

H2

(1)

H C3

H C3

(2)

H C3 CH3

(3)

CH3

CH3

(4) CH3

H C3

CH

3

CH3

O3

Zn+H2O CH

3

CH3

O

OHC

C

7182019 AIPMT2015 Solutions

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A L L E N

8

AIPMT 2 15

(1)

(2)

(3)

(4)

-

(1) -

(2)

(3) -

(4)

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1) (2)

(3) (4)

(1) ()(2)

(3)

(4)

-

(1) (2)

(3) (4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

( )

-

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

9

CODE F

-

(1) A

(2) A

(3)

A

(4) A

A

-

(1) (2)

(3) (4) C

A 983079A983079

983079B983079

(1) AB AB (2) ABAB

(3) (4) A B

-

(1) (2) -

(3) (4)

C

2011 -

(1) A (2)

(3) (4)

A -

(1)

(2)

(3) E

(4)

H

(1) (2) E (3) (4) F

Aring K C A G(5) (5) 5 (2) -

(1) (2)

(3) B (4) A

-

(1) B (2) I

(3) H (4) F

(1) G

(2)

HC

(3) A

(4) B983079

I DA 17

DA -

(1) G 17 A 165 325

(2) G 17 A 33 33

(3) G 85 A 50 245

(4) G 34 A 245 245

I B B

- -

(1) A H

(2) A -

(3)

(4) A H

C -

(1)

(2) C

(3)

(4)

(A E) -

(A)

(B)

(C) C C A

(D)

(E) I

(1) (B) (C) (D) (2) (A) (D) (E)(3) (B) (C) (E) (4) (A) (C) (D)

7182019 AIPMT2015 Solutions

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A L L E N

10

AIPMT 2 15

(1) = B + F

(2) = + BC + BC

(3) B = + BC + BC

(4) = B

-

(1) D (2)

(3) C (4) I

G I

G G

(1) I C A

(2) G E A C(3) C G

(4) B-

C983079

-

(1)

(2)

(3) E

(4)

G -

(1)

(2)

(3)

(4)

(1) I

(2) D

(3) I

(4) I

C -

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4) C

-

(1) (2)

(3) (4) A

G -

(1)

(2) C

(3) H

(4) C

-

(1) (2) D

(3) (4) H

DA -

(1) (2)

(3) (4) C

G E

I

(1)

(2)

(3) F

b-

(4)

(1) C (2) (3) A- (4) A

(1) G

(2)

(3) A

(4) G

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

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A L L E N

2

AIPMT 2 15

-

(1) 2+ - +2 2 2O lt O lt O (2) + - 2+

2 2 2O lt O lt O

(3) - + 2+2 2 2O lt O lt O (4) 2+ + -

2 2 2O lt O lt O

A (MO)

- + +

-

2

2 2 2O O O

N 17 15 14

B 15 25 30

A K+ C2+

I

(1) C2+ lt A lt K+ (2) C2+ lt K+ lt A

(3) K+ lt A lt C2+ (4) A lt K+ lt C2+

I

A micro

1

C+2 lt K+ lt A

(1) vsTI K

(2) I K

(3)

I K

(4) I K

A

-

= THORN = -l l

ER E

K A K A R

l1

K

(1) 2

3CO --

3CO (2)3 NO

-2-3SO

(3) 2

3 3ClO SO- - (4) 2 2

3 3CO SO- -

- -

-

2

3 3

3 3

CO SO

N 42 42

A 983079983079

C5H10O

I 983079 I

- 983079983079 -

(1) 2- (2) 3-

(3) - (4)

PNHNH2

I + NOH

I 2

983079

P

N

N

R-

(C H O)5 10

A CH3 CH

2 C CH

2 CH

3

O

CH3

CH2

C CH2 CH

3

O

reduction

Zn-HgHCl

or NH NH OH2 2

mdash -

CH mdashCH mdashCH mdashCH mdashCH3 2 2 2 3

n-pentane

(1)2 2 2O O O- +lt lt

(2) 2 2 2O O O- +

gt lt

(3)2 2 2O O O- +lt gt

(4)2 2 2O O O- +gt gt

A (MO)

- +

-2 2 2

O O O

N 17 16 15

B 15 2 25

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A L L E N

3

CODE F

O

(1) C

(2) C

(3) C

(4) C

O CH3LAring

CH3

O+

-

(1) A (2) A

(3) A (4) -A

NO

2

weakly acidic

reduction

NH2

aniline

NH OH

Phenyl hydroxyl amine

electrolytic

medium

strongly

acidic medium

NH2

OH

p-Aminophenol

nitrobenzene rearrangement

M 284 BM -

(A N = 28 = 22 C = 24 C = 27)

(1) 3+ (2) C2+ (3) C2+ (4) N2+

N

+2

= 3

8

() =2

Q ( )m = + 2

m = 28 BM

A

361 I

(1) 127 (2) 80

(3) 108 (4) 40

FCC = = =acute

361 127

2 141412 2

(1) H C C = C C C3

H

H H2

(2) H C C = C C C3

H

H H2

(3) H C C = C C C3

H

H H2

(4) H C C = C C C3

H

H H2

A C p

CH3

CH CH CH2

C

983079 H983079 () A2(SO4)3( 100 )

(1) K3F(CN)6 (2) A(NO3)3(3) K4F(CN)6 (4) K2SO4

H

( ) + -reg +3 2

2 4 43A SO 2A 3SO

= 5

( )[ ] ( )[ ]-+reg +4

6 64K F CN 4K F CN

=5 THORN = =5

N

(1)

(2)

(3) -

(4) 983079-983079

NO2

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A L L E N

4

AIPMT 2 15

p-

-

H H H

CH3

CH3

H C3

H C3

H C2 H

(1) 8 (2) 12 (3) 16 (4) 4

CH3

CH3

H

CH2

H

H

CH3

CH3

H p = 4

p = 8

S 983079

-(1) C gt S gt B gt M (2) S gt C gt M gt B

(3) B gt M gt S gt C (4) M gt C gt S gt B

D M+2 M+2

MSO gt CSO gt SSO gt BSO44 4 4

SH

M

(1)2 NO- (2)

2 NO+

(3)3 NO- (4)

2 NO

NO2+ ( = 180)

2 3 2 2NO NO NO NO

bond angle

- - +lt lt lt frac34frac34frac34frac34frac34frac34frac34reg

I

reaction is 16 times 1012

-

(1)

(2)

(3)

(4)

K = 16 1012

K -

- F2+ ( = 26)

(1) - C ( = 17)

(2) - F ( = 26)(3) - N ( = 10)

(4) - M ( = 12)

F+2 = 36 ( = 6)

C = 12 22 26 22 35

= 11 - F+2

I C - C

(1)

H C3

C C

H C3

CH3

(2)

CH CH

(3)O NH C2 2

H

C CH

(4)H C3

H C3

C C

H

C Cl

CH3

CH3 CH

3

Cl C+

CH3

CH3 CH

3

t-butyl carbonium ion

ClCH

H

Cl CH

H

Aring

benzyl carbonium ion

[stable due to resonance]

C Cl

H

O2NH

2C H

Cl C

H

O2NCH

2 H

-I effect

Aring

CCH

3

CH3

H

Cl Cl

CCH

3

CH3

H

Aring

Secondary carbonium ion

[isopropyl carbonium ion]

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A L L E N

5

CODE F

M

CH2

Aring

CH2

Aring

CH2

Aring CH2

Aring

A

-

(1) E (2) D

(3) N-C (4) F C

A

C

CH C CH 3

CH3

CH3

P C P

P

CH3

(I) (II) (III)

H I -

(1) II (2) III (3) I III (4) I

CHC

CH3

CH3

CH3

C

Ph

PhPh

CH3

H(I)

(II) (III)

O (III) H

CH CON+CH CH C3 3 2

CH3

CH3

CH COCH CH3 2 3

CH3

CH3

NC

-

(1)

(2) E

(3) G - K

(4) S

G

I

C (III)

25ordmC

(1) CC3middot4NH3 (2) CC3middot5NH3

(3) CC3middot6NH3 (4) CC3middot3NH3

( )eacute ugraveTHORN euml ucirc3 3 3 33CC 3NH C NH C

frac34frac34frac34frac34regeacute ugraveeuml ucirc3ANO

3 3 3C(NH ) C

A H2 O2 1 4 ()

(1) 4 1 (2) 16 1 (3) 2 1 (4) 1 4

= THORN = =2 2

2 2

H H

O O

1 1 2 4

4 4 32 1

(1) D CSO4 (2) F F(CO)5 F

(3) L H2

(4) R

( )[ ]+ reg0 05F 5CO F CO

N

B

(N )

(1) (40) N (41) (2) (40) H (72)

(3) (40) (73) (4) (22) (40)

D

H

(1) DG = 230 R K

(2) DGordm = 230 R K(3) DGordm = 230 R K

(4) DG = 230 R K

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A L L E N

6

AIPMT 2 15

D = -0G 230RK

DG =0

983079983079

-

(1) 2 h (2) 2 3 h (3) 0 h (4) 6 h

O = ( )+l l h1

- l=2

= ( )+ =h h2 2 1 6

02 1

(1) M

(2) M

(3)

(4)

( ) ( )D gt D

K

()

times times gt times times THORN gt

S

-

(1) M2+ (2) K+ (3) F2+ (4) C2+

K+

G -

H C3 H C3 H C2C H 3 C H 2 C H 2

C H 3 C H 3 C H 2

( I ) ( I I ) ( I I I )

-

(1) III gt II gt I (2) II gt III gt I

(3) II gt I gt III (4) I gt II gt III

R CH CH R + H2

R CH2 CH

2 R +

(1 mole)

DH

micro1

-

H C3

C CC C

OH O

C CO O

H H2

OC H2 5

H C3

OC H2 5

(1) 16 1 -

(2) 9 2 -

(3) 9 1 -

(4) 18 2 -

H

CH

H

C

O H

C

H

C

O

O C

H

H

C

H

H

H

18 s + 2p

B

-

(1) PHB

(2) B - N

(3) N 6 6

(4) N 2- 6

N 2-N-6

(NH2 CH

2 COOH)

NH2 (CH

2)5COOH

s- p- -

(1) O4 (2) (CN)2(3) CH2(CN)2 (4) HCO3

7182019 AIPMT2015 Solutions

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A L L E N

7

CODE F

O

OO O

s = 4 p = 4

C(CN)63 -

(1) C(CN)63

-

(2) C(CN)63

(3) C(CN)63

- (4) C(CN)63

-

C(CN)6 3

C+3 = 36 40 40

Q

-

(1) DS (2) D

(3) DP = P - PR (4) DH

F DS

gt 0

-

(1) E (2) E-

(3) (4) C

G -

CH3

(I) (II) (III)

CH3CH3

CH3 CH3

CH3

OOO

(1) I III (2) II III(3) I II III (4) I II

CH3

CH3

O

H

CH3

CH3

OH

O

CH3

CH3

OH

CH3

CH3

H

O

CH3

CH3

OH

CH3

CH3

H

-

-

(1) F

(2) S

(3) M

(4)

=12

0693

K

12

A -

OHCC

CC

CH

CH3

H2

O

CH3

H2

(1)

H C3

H C3

(2)

H C3 CH3

(3)

CH3

CH3

(4) CH3

H C3

CH

3

CH3

O3

Zn+H2O CH

3

CH3

O

OHC

C

7182019 AIPMT2015 Solutions

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A L L E N

8

AIPMT 2 15

(1)

(2)

(3)

(4)

-

(1) -

(2)

(3) -

(4)

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1) (2)

(3) (4)

(1) ()(2)

(3)

(4)

-

(1) (2)

(3) (4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

( )

-

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

9

CODE F

-

(1) A

(2) A

(3)

A

(4) A

A

-

(1) (2)

(3) (4) C

A 983079A983079

983079B983079

(1) AB AB (2) ABAB

(3) (4) A B

-

(1) (2) -

(3) (4)

C

2011 -

(1) A (2)

(3) (4)

A -

(1)

(2)

(3) E

(4)

H

(1) (2) E (3) (4) F

Aring K C A G(5) (5) 5 (2) -

(1) (2)

(3) B (4) A

-

(1) B (2) I

(3) H (4) F

(1) G

(2)

HC

(3) A

(4) B983079

I DA 17

DA -

(1) G 17 A 165 325

(2) G 17 A 33 33

(3) G 85 A 50 245

(4) G 34 A 245 245

I B B

- -

(1) A H

(2) A -

(3)

(4) A H

C -

(1)

(2) C

(3)

(4)

(A E) -

(A)

(B)

(C) C C A

(D)

(E) I

(1) (B) (C) (D) (2) (A) (D) (E)(3) (B) (C) (E) (4) (A) (C) (D)

7182019 AIPMT2015 Solutions

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A L L E N

10

AIPMT 2 15

(1) = B + F

(2) = + BC + BC

(3) B = + BC + BC

(4) = B

-

(1) D (2)

(3) C (4) I

G I

G G

(1) I C A

(2) G E A C(3) C G

(4) B-

C983079

-

(1)

(2)

(3) E

(4)

G -

(1)

(2)

(3)

(4)

(1) I

(2) D

(3) I

(4) I

C -

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4) C

-

(1) (2)

(3) (4) A

G -

(1)

(2) C

(3) H

(4) C

-

(1) (2) D

(3) (4) H

DA -

(1) (2)

(3) (4) C

G E

I

(1)

(2)

(3) F

b-

(4)

(1) C (2) (3) A- (4) A

(1) G

(2)

(3) A

(4) G

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

3

CODE F

O

(1) C

(2) C

(3) C

(4) C

O CH3LAring

CH3

O+

-

(1) A (2) A

(3) A (4) -A

NO

2

weakly acidic

reduction

NH2

aniline

NH OH

Phenyl hydroxyl amine

electrolytic

medium

strongly

acidic medium

NH2

OH

p-Aminophenol

nitrobenzene rearrangement

M 284 BM -

(A N = 28 = 22 C = 24 C = 27)

(1) 3+ (2) C2+ (3) C2+ (4) N2+

N

+2

= 3

8

() =2

Q ( )m = + 2

m = 28 BM

A

361 I

(1) 127 (2) 80

(3) 108 (4) 40

FCC = = =acute

361 127

2 141412 2

(1) H C C = C C C3

H

H H2

(2) H C C = C C C3

H

H H2

(3) H C C = C C C3

H

H H2

(4) H C C = C C C3

H

H H2

A C p

CH3

CH CH CH2

C

983079 H983079 () A2(SO4)3( 100 )

(1) K3F(CN)6 (2) A(NO3)3(3) K4F(CN)6 (4) K2SO4

H

( ) + -reg +3 2

2 4 43A SO 2A 3SO

= 5

( )[ ] ( )[ ]-+reg +4

6 64K F CN 4K F CN

=5 THORN = =5

N

(1)

(2)

(3) -

(4) 983079-983079

NO2

7182019 AIPMT2015 Solutions

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A L L E N

4

AIPMT 2 15

p-

-

H H H

CH3

CH3

H C3

H C3

H C2 H

(1) 8 (2) 12 (3) 16 (4) 4

CH3

CH3

H

CH2

H

H

CH3

CH3

H p = 4

p = 8

S 983079

-(1) C gt S gt B gt M (2) S gt C gt M gt B

(3) B gt M gt S gt C (4) M gt C gt S gt B

D M+2 M+2

MSO gt CSO gt SSO gt BSO44 4 4

SH

M

(1)2 NO- (2)

2 NO+

(3)3 NO- (4)

2 NO

NO2+ ( = 180)

2 3 2 2NO NO NO NO

bond angle

- - +lt lt lt frac34frac34frac34frac34frac34frac34frac34reg

I

reaction is 16 times 1012

-

(1)

(2)

(3)

(4)

K = 16 1012

K -

- F2+ ( = 26)

(1) - C ( = 17)

(2) - F ( = 26)(3) - N ( = 10)

(4) - M ( = 12)

F+2 = 36 ( = 6)

C = 12 22 26 22 35

= 11 - F+2

I C - C

(1)

H C3

C C

H C3

CH3

(2)

CH CH

(3)O NH C2 2

H

C CH

(4)H C3

H C3

C C

H

C Cl

CH3

CH3 CH

3

Cl C+

CH3

CH3 CH

3

t-butyl carbonium ion

ClCH

H

Cl CH

H

Aring

benzyl carbonium ion

[stable due to resonance]

C Cl

H

O2NH

2C H

Cl C

H

O2NCH

2 H

-I effect

Aring

CCH

3

CH3

H

Cl Cl

CCH

3

CH3

H

Aring

Secondary carbonium ion

[isopropyl carbonium ion]

7182019 AIPMT2015 Solutions

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A L L E N

5

CODE F

M

CH2

Aring

CH2

Aring

CH2

Aring CH2

Aring

A

-

(1) E (2) D

(3) N-C (4) F C

A

C

CH C CH 3

CH3

CH3

P C P

P

CH3

(I) (II) (III)

H I -

(1) II (2) III (3) I III (4) I

CHC

CH3

CH3

CH3

C

Ph

PhPh

CH3

H(I)

(II) (III)

O (III) H

CH CON+CH CH C3 3 2

CH3

CH3

CH COCH CH3 2 3

CH3

CH3

NC

-

(1)

(2) E

(3) G - K

(4) S

G

I

C (III)

25ordmC

(1) CC3middot4NH3 (2) CC3middot5NH3

(3) CC3middot6NH3 (4) CC3middot3NH3

( )eacute ugraveTHORN euml ucirc3 3 3 33CC 3NH C NH C

frac34frac34frac34frac34regeacute ugraveeuml ucirc3ANO

3 3 3C(NH ) C

A H2 O2 1 4 ()

(1) 4 1 (2) 16 1 (3) 2 1 (4) 1 4

= THORN = =2 2

2 2

H H

O O

1 1 2 4

4 4 32 1

(1) D CSO4 (2) F F(CO)5 F

(3) L H2

(4) R

( )[ ]+ reg0 05F 5CO F CO

N

B

(N )

(1) (40) N (41) (2) (40) H (72)

(3) (40) (73) (4) (22) (40)

D

H

(1) DG = 230 R K

(2) DGordm = 230 R K(3) DGordm = 230 R K

(4) DG = 230 R K

7182019 AIPMT2015 Solutions

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A L L E N

6

AIPMT 2 15

D = -0G 230RK

DG =0

983079983079

-

(1) 2 h (2) 2 3 h (3) 0 h (4) 6 h

O = ( )+l l h1

- l=2

= ( )+ =h h2 2 1 6

02 1

(1) M

(2) M

(3)

(4)

( ) ( )D gt D

K

()

times times gt times times THORN gt

S

-

(1) M2+ (2) K+ (3) F2+ (4) C2+

K+

G -

H C3 H C3 H C2C H 3 C H 2 C H 2

C H 3 C H 3 C H 2

( I ) ( I I ) ( I I I )

-

(1) III gt II gt I (2) II gt III gt I

(3) II gt I gt III (4) I gt II gt III

R CH CH R + H2

R CH2 CH

2 R +

(1 mole)

DH

micro1

-

H C3

C CC C

OH O

C CO O

H H2

OC H2 5

H C3

OC H2 5

(1) 16 1 -

(2) 9 2 -

(3) 9 1 -

(4) 18 2 -

H

CH

H

C

O H

C

H

C

O

O C

H

H

C

H

H

H

18 s + 2p

B

-

(1) PHB

(2) B - N

(3) N 6 6

(4) N 2- 6

N 2-N-6

(NH2 CH

2 COOH)

NH2 (CH

2)5COOH

s- p- -

(1) O4 (2) (CN)2(3) CH2(CN)2 (4) HCO3

7182019 AIPMT2015 Solutions

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A L L E N

7

CODE F

O

OO O

s = 4 p = 4

C(CN)63 -

(1) C(CN)63

-

(2) C(CN)63

(3) C(CN)63

- (4) C(CN)63

-

C(CN)6 3

C+3 = 36 40 40

Q

-

(1) DS (2) D

(3) DP = P - PR (4) DH

F DS

gt 0

-

(1) E (2) E-

(3) (4) C

G -

CH3

(I) (II) (III)

CH3CH3

CH3 CH3

CH3

OOO

(1) I III (2) II III(3) I II III (4) I II

CH3

CH3

O

H

CH3

CH3

OH

O

CH3

CH3

OH

CH3

CH3

H

O

CH3

CH3

OH

CH3

CH3

H

-

-

(1) F

(2) S

(3) M

(4)

=12

0693

K

12

A -

OHCC

CC

CH

CH3

H2

O

CH3

H2

(1)

H C3

H C3

(2)

H C3 CH3

(3)

CH3

CH3

(4) CH3

H C3

CH

3

CH3

O3

Zn+H2O CH

3

CH3

O

OHC

C

7182019 AIPMT2015 Solutions

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A L L E N

8

AIPMT 2 15

(1)

(2)

(3)

(4)

-

(1) -

(2)

(3) -

(4)

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1) (2)

(3) (4)

(1) ()(2)

(3)

(4)

-

(1) (2)

(3) (4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

( )

-

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

9

CODE F

-

(1) A

(2) A

(3)

A

(4) A

A

-

(1) (2)

(3) (4) C

A 983079A983079

983079B983079

(1) AB AB (2) ABAB

(3) (4) A B

-

(1) (2) -

(3) (4)

C

2011 -

(1) A (2)

(3) (4)

A -

(1)

(2)

(3) E

(4)

H

(1) (2) E (3) (4) F

Aring K C A G(5) (5) 5 (2) -

(1) (2)

(3) B (4) A

-

(1) B (2) I

(3) H (4) F

(1) G

(2)

HC

(3) A

(4) B983079

I DA 17

DA -

(1) G 17 A 165 325

(2) G 17 A 33 33

(3) G 85 A 50 245

(4) G 34 A 245 245

I B B

- -

(1) A H

(2) A -

(3)

(4) A H

C -

(1)

(2) C

(3)

(4)

(A E) -

(A)

(B)

(C) C C A

(D)

(E) I

(1) (B) (C) (D) (2) (A) (D) (E)(3) (B) (C) (E) (4) (A) (C) (D)

7182019 AIPMT2015 Solutions

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A L L E N

10

AIPMT 2 15

(1) = B + F

(2) = + BC + BC

(3) B = + BC + BC

(4) = B

-

(1) D (2)

(3) C (4) I

G I

G G

(1) I C A

(2) G E A C(3) C G

(4) B-

C983079

-

(1)

(2)

(3) E

(4)

G -

(1)

(2)

(3)

(4)

(1) I

(2) D

(3) I

(4) I

C -

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4) C

-

(1) (2)

(3) (4) A

G -

(1)

(2) C

(3) H

(4) C

-

(1) (2) D

(3) (4) H

DA -

(1) (2)

(3) (4) C

G E

I

(1)

(2)

(3) F

b-

(4)

(1) C (2) (3) A- (4) A

(1) G

(2)

(3) A

(4) G

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

4

AIPMT 2 15

p-

-

H H H

CH3

CH3

H C3

H C3

H C2 H

(1) 8 (2) 12 (3) 16 (4) 4

CH3

CH3

H

CH2

H

H

CH3

CH3

H p = 4

p = 8

S 983079

-(1) C gt S gt B gt M (2) S gt C gt M gt B

(3) B gt M gt S gt C (4) M gt C gt S gt B

D M+2 M+2

MSO gt CSO gt SSO gt BSO44 4 4

SH

M

(1)2 NO- (2)

2 NO+

(3)3 NO- (4)

2 NO

NO2+ ( = 180)

2 3 2 2NO NO NO NO

bond angle

- - +lt lt lt frac34frac34frac34frac34frac34frac34frac34reg

I

reaction is 16 times 1012

-

(1)

(2)

(3)

(4)

K = 16 1012

K -

- F2+ ( = 26)

(1) - C ( = 17)

(2) - F ( = 26)(3) - N ( = 10)

(4) - M ( = 12)

F+2 = 36 ( = 6)

C = 12 22 26 22 35

= 11 - F+2

I C - C

(1)

H C3

C C

H C3

CH3

(2)

CH CH

(3)O NH C2 2

H

C CH

(4)H C3

H C3

C C

H

C Cl

CH3

CH3 CH

3

Cl C+

CH3

CH3 CH

3

t-butyl carbonium ion

ClCH

H

Cl CH

H

Aring

benzyl carbonium ion

[stable due to resonance]

C Cl

H

O2NH

2C H

Cl C

H

O2NCH

2 H

-I effect

Aring

CCH

3

CH3

H

Cl Cl

CCH

3

CH3

H

Aring

Secondary carbonium ion

[isopropyl carbonium ion]

7182019 AIPMT2015 Solutions

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A L L E N

5

CODE F

M

CH2

Aring

CH2

Aring

CH2

Aring CH2

Aring

A

-

(1) E (2) D

(3) N-C (4) F C

A

C

CH C CH 3

CH3

CH3

P C P

P

CH3

(I) (II) (III)

H I -

(1) II (2) III (3) I III (4) I

CHC

CH3

CH3

CH3

C

Ph

PhPh

CH3

H(I)

(II) (III)

O (III) H

CH CON+CH CH C3 3 2

CH3

CH3

CH COCH CH3 2 3

CH3

CH3

NC

-

(1)

(2) E

(3) G - K

(4) S

G

I

C (III)

25ordmC

(1) CC3middot4NH3 (2) CC3middot5NH3

(3) CC3middot6NH3 (4) CC3middot3NH3

( )eacute ugraveTHORN euml ucirc3 3 3 33CC 3NH C NH C

frac34frac34frac34frac34regeacute ugraveeuml ucirc3ANO

3 3 3C(NH ) C

A H2 O2 1 4 ()

(1) 4 1 (2) 16 1 (3) 2 1 (4) 1 4

= THORN = =2 2

2 2

H H

O O

1 1 2 4

4 4 32 1

(1) D CSO4 (2) F F(CO)5 F

(3) L H2

(4) R

( )[ ]+ reg0 05F 5CO F CO

N

B

(N )

(1) (40) N (41) (2) (40) H (72)

(3) (40) (73) (4) (22) (40)

D

H

(1) DG = 230 R K

(2) DGordm = 230 R K(3) DGordm = 230 R K

(4) DG = 230 R K

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A L L E N

6

AIPMT 2 15

D = -0G 230RK

DG =0

983079983079

-

(1) 2 h (2) 2 3 h (3) 0 h (4) 6 h

O = ( )+l l h1

- l=2

= ( )+ =h h2 2 1 6

02 1

(1) M

(2) M

(3)

(4)

( ) ( )D gt D

K

()

times times gt times times THORN gt

S

-

(1) M2+ (2) K+ (3) F2+ (4) C2+

K+

G -

H C3 H C3 H C2C H 3 C H 2 C H 2

C H 3 C H 3 C H 2

( I ) ( I I ) ( I I I )

-

(1) III gt II gt I (2) II gt III gt I

(3) II gt I gt III (4) I gt II gt III

R CH CH R + H2

R CH2 CH

2 R +

(1 mole)

DH

micro1

-

H C3

C CC C

OH O

C CO O

H H2

OC H2 5

H C3

OC H2 5

(1) 16 1 -

(2) 9 2 -

(3) 9 1 -

(4) 18 2 -

H

CH

H

C

O H

C

H

C

O

O C

H

H

C

H

H

H

18 s + 2p

B

-

(1) PHB

(2) B - N

(3) N 6 6

(4) N 2- 6

N 2-N-6

(NH2 CH

2 COOH)

NH2 (CH

2)5COOH

s- p- -

(1) O4 (2) (CN)2(3) CH2(CN)2 (4) HCO3

7182019 AIPMT2015 Solutions

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A L L E N

7

CODE F

O

OO O

s = 4 p = 4

C(CN)63 -

(1) C(CN)63

-

(2) C(CN)63

(3) C(CN)63

- (4) C(CN)63

-

C(CN)6 3

C+3 = 36 40 40

Q

-

(1) DS (2) D

(3) DP = P - PR (4) DH

F DS

gt 0

-

(1) E (2) E-

(3) (4) C

G -

CH3

(I) (II) (III)

CH3CH3

CH3 CH3

CH3

OOO

(1) I III (2) II III(3) I II III (4) I II

CH3

CH3

O

H

CH3

CH3

OH

O

CH3

CH3

OH

CH3

CH3

H

O

CH3

CH3

OH

CH3

CH3

H

-

-

(1) F

(2) S

(3) M

(4)

=12

0693

K

12

A -

OHCC

CC

CH

CH3

H2

O

CH3

H2

(1)

H C3

H C3

(2)

H C3 CH3

(3)

CH3

CH3

(4) CH3

H C3

CH

3

CH3

O3

Zn+H2O CH

3

CH3

O

OHC

C

7182019 AIPMT2015 Solutions

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A L L E N

8

AIPMT 2 15

(1)

(2)

(3)

(4)

-

(1) -

(2)

(3) -

(4)

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1) (2)

(3) (4)

(1) ()(2)

(3)

(4)

-

(1) (2)

(3) (4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

( )

-

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

9

CODE F

-

(1) A

(2) A

(3)

A

(4) A

A

-

(1) (2)

(3) (4) C

A 983079A983079

983079B983079

(1) AB AB (2) ABAB

(3) (4) A B

-

(1) (2) -

(3) (4)

C

2011 -

(1) A (2)

(3) (4)

A -

(1)

(2)

(3) E

(4)

H

(1) (2) E (3) (4) F

Aring K C A G(5) (5) 5 (2) -

(1) (2)

(3) B (4) A

-

(1) B (2) I

(3) H (4) F

(1) G

(2)

HC

(3) A

(4) B983079

I DA 17

DA -

(1) G 17 A 165 325

(2) G 17 A 33 33

(3) G 85 A 50 245

(4) G 34 A 245 245

I B B

- -

(1) A H

(2) A -

(3)

(4) A H

C -

(1)

(2) C

(3)

(4)

(A E) -

(A)

(B)

(C) C C A

(D)

(E) I

(1) (B) (C) (D) (2) (A) (D) (E)(3) (B) (C) (E) (4) (A) (C) (D)

7182019 AIPMT2015 Solutions

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A L L E N

10

AIPMT 2 15

(1) = B + F

(2) = + BC + BC

(3) B = + BC + BC

(4) = B

-

(1) D (2)

(3) C (4) I

G I

G G

(1) I C A

(2) G E A C(3) C G

(4) B-

C983079

-

(1)

(2)

(3) E

(4)

G -

(1)

(2)

(3)

(4)

(1) I

(2) D

(3) I

(4) I

C -

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4) C

-

(1) (2)

(3) (4) A

G -

(1)

(2) C

(3) H

(4) C

-

(1) (2) D

(3) (4) H

DA -

(1) (2)

(3) (4) C

G E

I

(1)

(2)

(3) F

b-

(4)

(1) C (2) (3) A- (4) A

(1) G

(2)

(3) A

(4) G

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

5

CODE F

M

CH2

Aring

CH2

Aring

CH2

Aring CH2

Aring

A

-

(1) E (2) D

(3) N-C (4) F C

A

C

CH C CH 3

CH3

CH3

P C P

P

CH3

(I) (II) (III)

H I -

(1) II (2) III (3) I III (4) I

CHC

CH3

CH3

CH3

C

Ph

PhPh

CH3

H(I)

(II) (III)

O (III) H

CH CON+CH CH C3 3 2

CH3

CH3

CH COCH CH3 2 3

CH3

CH3

NC

-

(1)

(2) E

(3) G - K

(4) S

G

I

C (III)

25ordmC

(1) CC3middot4NH3 (2) CC3middot5NH3

(3) CC3middot6NH3 (4) CC3middot3NH3

( )eacute ugraveTHORN euml ucirc3 3 3 33CC 3NH C NH C

frac34frac34frac34frac34regeacute ugraveeuml ucirc3ANO

3 3 3C(NH ) C

A H2 O2 1 4 ()

(1) 4 1 (2) 16 1 (3) 2 1 (4) 1 4

= THORN = =2 2

2 2

H H

O O

1 1 2 4

4 4 32 1

(1) D CSO4 (2) F F(CO)5 F

(3) L H2

(4) R

( )[ ]+ reg0 05F 5CO F CO

N

B

(N )

(1) (40) N (41) (2) (40) H (72)

(3) (40) (73) (4) (22) (40)

D

H

(1) DG = 230 R K

(2) DGordm = 230 R K(3) DGordm = 230 R K

(4) DG = 230 R K

7182019 AIPMT2015 Solutions

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A L L E N

6

AIPMT 2 15

D = -0G 230RK

DG =0

983079983079

-

(1) 2 h (2) 2 3 h (3) 0 h (4) 6 h

O = ( )+l l h1

- l=2

= ( )+ =h h2 2 1 6

02 1

(1) M

(2) M

(3)

(4)

( ) ( )D gt D

K

()

times times gt times times THORN gt

S

-

(1) M2+ (2) K+ (3) F2+ (4) C2+

K+

G -

H C3 H C3 H C2C H 3 C H 2 C H 2

C H 3 C H 3 C H 2

( I ) ( I I ) ( I I I )

-

(1) III gt II gt I (2) II gt III gt I

(3) II gt I gt III (4) I gt II gt III

R CH CH R + H2

R CH2 CH

2 R +

(1 mole)

DH

micro1

-

H C3

C CC C

OH O

C CO O

H H2

OC H2 5

H C3

OC H2 5

(1) 16 1 -

(2) 9 2 -

(3) 9 1 -

(4) 18 2 -

H

CH

H

C

O H

C

H

C

O

O C

H

H

C

H

H

H

18 s + 2p

B

-

(1) PHB

(2) B - N

(3) N 6 6

(4) N 2- 6

N 2-N-6

(NH2 CH

2 COOH)

NH2 (CH

2)5COOH

s- p- -

(1) O4 (2) (CN)2(3) CH2(CN)2 (4) HCO3

7182019 AIPMT2015 Solutions

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A L L E N

7

CODE F

O

OO O

s = 4 p = 4

C(CN)63 -

(1) C(CN)63

-

(2) C(CN)63

(3) C(CN)63

- (4) C(CN)63

-

C(CN)6 3

C+3 = 36 40 40

Q

-

(1) DS (2) D

(3) DP = P - PR (4) DH

F DS

gt 0

-

(1) E (2) E-

(3) (4) C

G -

CH3

(I) (II) (III)

CH3CH3

CH3 CH3

CH3

OOO

(1) I III (2) II III(3) I II III (4) I II

CH3

CH3

O

H

CH3

CH3

OH

O

CH3

CH3

OH

CH3

CH3

H

O

CH3

CH3

OH

CH3

CH3

H

-

-

(1) F

(2) S

(3) M

(4)

=12

0693

K

12

A -

OHCC

CC

CH

CH3

H2

O

CH3

H2

(1)

H C3

H C3

(2)

H C3 CH3

(3)

CH3

CH3

(4) CH3

H C3

CH

3

CH3

O3

Zn+H2O CH

3

CH3

O

OHC

C

7182019 AIPMT2015 Solutions

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A L L E N

8

AIPMT 2 15

(1)

(2)

(3)

(4)

-

(1) -

(2)

(3) -

(4)

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1) (2)

(3) (4)

(1) ()(2)

(3)

(4)

-

(1) (2)

(3) (4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

( )

-

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

9

CODE F

-

(1) A

(2) A

(3)

A

(4) A

A

-

(1) (2)

(3) (4) C

A 983079A983079

983079B983079

(1) AB AB (2) ABAB

(3) (4) A B

-

(1) (2) -

(3) (4)

C

2011 -

(1) A (2)

(3) (4)

A -

(1)

(2)

(3) E

(4)

H

(1) (2) E (3) (4) F

Aring K C A G(5) (5) 5 (2) -

(1) (2)

(3) B (4) A

-

(1) B (2) I

(3) H (4) F

(1) G

(2)

HC

(3) A

(4) B983079

I DA 17

DA -

(1) G 17 A 165 325

(2) G 17 A 33 33

(3) G 85 A 50 245

(4) G 34 A 245 245

I B B

- -

(1) A H

(2) A -

(3)

(4) A H

C -

(1)

(2) C

(3)

(4)

(A E) -

(A)

(B)

(C) C C A

(D)

(E) I

(1) (B) (C) (D) (2) (A) (D) (E)(3) (B) (C) (E) (4) (A) (C) (D)

7182019 AIPMT2015 Solutions

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A L L E N

10

AIPMT 2 15

(1) = B + F

(2) = + BC + BC

(3) B = + BC + BC

(4) = B

-

(1) D (2)

(3) C (4) I

G I

G G

(1) I C A

(2) G E A C(3) C G

(4) B-

C983079

-

(1)

(2)

(3) E

(4)

G -

(1)

(2)

(3)

(4)

(1) I

(2) D

(3) I

(4) I

C -

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4) C

-

(1) (2)

(3) (4) A

G -

(1)

(2) C

(3) H

(4) C

-

(1) (2) D

(3) (4) H

DA -

(1) (2)

(3) (4) C

G E

I

(1)

(2)

(3) F

b-

(4)

(1) C (2) (3) A- (4) A

(1) G

(2)

(3) A

(4) G

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

6

AIPMT 2 15

D = -0G 230RK

DG =0

983079983079

-

(1) 2 h (2) 2 3 h (3) 0 h (4) 6 h

O = ( )+l l h1

- l=2

= ( )+ =h h2 2 1 6

02 1

(1) M

(2) M

(3)

(4)

( ) ( )D gt D

K

()

times times gt times times THORN gt

S

-

(1) M2+ (2) K+ (3) F2+ (4) C2+

K+

G -

H C3 H C3 H C2C H 3 C H 2 C H 2

C H 3 C H 3 C H 2

( I ) ( I I ) ( I I I )

-

(1) III gt II gt I (2) II gt III gt I

(3) II gt I gt III (4) I gt II gt III

R CH CH R + H2

R CH2 CH

2 R +

(1 mole)

DH

micro1

-

H C3

C CC C

OH O

C CO O

H H2

OC H2 5

H C3

OC H2 5

(1) 16 1 -

(2) 9 2 -

(3) 9 1 -

(4) 18 2 -

H

CH

H

C

O H

C

H

C

O

O C

H

H

C

H

H

H

18 s + 2p

B

-

(1) PHB

(2) B - N

(3) N 6 6

(4) N 2- 6

N 2-N-6

(NH2 CH

2 COOH)

NH2 (CH

2)5COOH

s- p- -

(1) O4 (2) (CN)2(3) CH2(CN)2 (4) HCO3

7182019 AIPMT2015 Solutions

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A L L E N

7

CODE F

O

OO O

s = 4 p = 4

C(CN)63 -

(1) C(CN)63

-

(2) C(CN)63

(3) C(CN)63

- (4) C(CN)63

-

C(CN)6 3

C+3 = 36 40 40

Q

-

(1) DS (2) D

(3) DP = P - PR (4) DH

F DS

gt 0

-

(1) E (2) E-

(3) (4) C

G -

CH3

(I) (II) (III)

CH3CH3

CH3 CH3

CH3

OOO

(1) I III (2) II III(3) I II III (4) I II

CH3

CH3

O

H

CH3

CH3

OH

O

CH3

CH3

OH

CH3

CH3

H

O

CH3

CH3

OH

CH3

CH3

H

-

-

(1) F

(2) S

(3) M

(4)

=12

0693

K

12

A -

OHCC

CC

CH

CH3

H2

O

CH3

H2

(1)

H C3

H C3

(2)

H C3 CH3

(3)

CH3

CH3

(4) CH3

H C3

CH

3

CH3

O3

Zn+H2O CH

3

CH3

O

OHC

C

7182019 AIPMT2015 Solutions

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A L L E N

8

AIPMT 2 15

(1)

(2)

(3)

(4)

-

(1) -

(2)

(3) -

(4)

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1) (2)

(3) (4)

(1) ()(2)

(3)

(4)

-

(1) (2)

(3) (4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

( )

-

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

9

CODE F

-

(1) A

(2) A

(3)

A

(4) A

A

-

(1) (2)

(3) (4) C

A 983079A983079

983079B983079

(1) AB AB (2) ABAB

(3) (4) A B

-

(1) (2) -

(3) (4)

C

2011 -

(1) A (2)

(3) (4)

A -

(1)

(2)

(3) E

(4)

H

(1) (2) E (3) (4) F

Aring K C A G(5) (5) 5 (2) -

(1) (2)

(3) B (4) A

-

(1) B (2) I

(3) H (4) F

(1) G

(2)

HC

(3) A

(4) B983079

I DA 17

DA -

(1) G 17 A 165 325

(2) G 17 A 33 33

(3) G 85 A 50 245

(4) G 34 A 245 245

I B B

- -

(1) A H

(2) A -

(3)

(4) A H

C -

(1)

(2) C

(3)

(4)

(A E) -

(A)

(B)

(C) C C A

(D)

(E) I

(1) (B) (C) (D) (2) (A) (D) (E)(3) (B) (C) (E) (4) (A) (C) (D)

7182019 AIPMT2015 Solutions

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A L L E N

10

AIPMT 2 15

(1) = B + F

(2) = + BC + BC

(3) B = + BC + BC

(4) = B

-

(1) D (2)

(3) C (4) I

G I

G G

(1) I C A

(2) G E A C(3) C G

(4) B-

C983079

-

(1)

(2)

(3) E

(4)

G -

(1)

(2)

(3)

(4)

(1) I

(2) D

(3) I

(4) I

C -

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4) C

-

(1) (2)

(3) (4) A

G -

(1)

(2) C

(3) H

(4) C

-

(1) (2) D

(3) (4) H

DA -

(1) (2)

(3) (4) C

G E

I

(1)

(2)

(3) F

b-

(4)

(1) C (2) (3) A- (4) A

(1) G

(2)

(3) A

(4) G

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

7

CODE F

O

OO O

s = 4 p = 4

C(CN)63 -

(1) C(CN)63

-

(2) C(CN)63

(3) C(CN)63

- (4) C(CN)63

-

C(CN)6 3

C+3 = 36 40 40

Q

-

(1) DS (2) D

(3) DP = P - PR (4) DH

F DS

gt 0

-

(1) E (2) E-

(3) (4) C

G -

CH3

(I) (II) (III)

CH3CH3

CH3 CH3

CH3

OOO

(1) I III (2) II III(3) I II III (4) I II

CH3

CH3

O

H

CH3

CH3

OH

O

CH3

CH3

OH

CH3

CH3

H

O

CH3

CH3

OH

CH3

CH3

H

-

-

(1) F

(2) S

(3) M

(4)

=12

0693

K

12

A -

OHCC

CC

CH

CH3

H2

O

CH3

H2

(1)

H C3

H C3

(2)

H C3 CH3

(3)

CH3

CH3

(4) CH3

H C3

CH

3

CH3

O3

Zn+H2O CH

3

CH3

O

OHC

C

7182019 AIPMT2015 Solutions

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A L L E N

8

AIPMT 2 15

(1)

(2)

(3)

(4)

-

(1) -

(2)

(3) -

(4)

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1) (2)

(3) (4)

(1) ()(2)

(3)

(4)

-

(1) (2)

(3) (4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

( )

-

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

9

CODE F

-

(1) A

(2) A

(3)

A

(4) A

A

-

(1) (2)

(3) (4) C

A 983079A983079

983079B983079

(1) AB AB (2) ABAB

(3) (4) A B

-

(1) (2) -

(3) (4)

C

2011 -

(1) A (2)

(3) (4)

A -

(1)

(2)

(3) E

(4)

H

(1) (2) E (3) (4) F

Aring K C A G(5) (5) 5 (2) -

(1) (2)

(3) B (4) A

-

(1) B (2) I

(3) H (4) F

(1) G

(2)

HC

(3) A

(4) B983079

I DA 17

DA -

(1) G 17 A 165 325

(2) G 17 A 33 33

(3) G 85 A 50 245

(4) G 34 A 245 245

I B B

- -

(1) A H

(2) A -

(3)

(4) A H

C -

(1)

(2) C

(3)

(4)

(A E) -

(A)

(B)

(C) C C A

(D)

(E) I

(1) (B) (C) (D) (2) (A) (D) (E)(3) (B) (C) (E) (4) (A) (C) (D)

7182019 AIPMT2015 Solutions

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A L L E N

10

AIPMT 2 15

(1) = B + F

(2) = + BC + BC

(3) B = + BC + BC

(4) = B

-

(1) D (2)

(3) C (4) I

G I

G G

(1) I C A

(2) G E A C(3) C G

(4) B-

C983079

-

(1)

(2)

(3) E

(4)

G -

(1)

(2)

(3)

(4)

(1) I

(2) D

(3) I

(4) I

C -

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4) C

-

(1) (2)

(3) (4) A

G -

(1)

(2) C

(3) H

(4) C

-

(1) (2) D

(3) (4) H

DA -

(1) (2)

(3) (4) C

G E

I

(1)

(2)

(3) F

b-

(4)

(1) C (2) (3) A- (4) A

(1) G

(2)

(3) A

(4) G

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

8

AIPMT 2 15

(1)

(2)

(3)

(4)

-

(1) -

(2)

(3) -

(4)

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

(1) (2)

(3) (4)

(1) ()(2)

(3)

(4)

-

(1) (2)

(3) (4)

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

( )

-

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

9

CODE F

-

(1) A

(2) A

(3)

A

(4) A

A

-

(1) (2)

(3) (4) C

A 983079A983079

983079B983079

(1) AB AB (2) ABAB

(3) (4) A B

-

(1) (2) -

(3) (4)

C

2011 -

(1) A (2)

(3) (4)

A -

(1)

(2)

(3) E

(4)

H

(1) (2) E (3) (4) F

Aring K C A G(5) (5) 5 (2) -

(1) (2)

(3) B (4) A

-

(1) B (2) I

(3) H (4) F

(1) G

(2)

HC

(3) A

(4) B983079

I DA 17

DA -

(1) G 17 A 165 325

(2) G 17 A 33 33

(3) G 85 A 50 245

(4) G 34 A 245 245

I B B

- -

(1) A H

(2) A -

(3)

(4) A H

C -

(1)

(2) C

(3)

(4)

(A E) -

(A)

(B)

(C) C C A

(D)

(E) I

(1) (B) (C) (D) (2) (A) (D) (E)(3) (B) (C) (E) (4) (A) (C) (D)

7182019 AIPMT2015 Solutions

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A L L E N

10

AIPMT 2 15

(1) = B + F

(2) = + BC + BC

(3) B = + BC + BC

(4) = B

-

(1) D (2)

(3) C (4) I

G I

G G

(1) I C A

(2) G E A C(3) C G

(4) B-

C983079

-

(1)

(2)

(3) E

(4)

G -

(1)

(2)

(3)

(4)

(1) I

(2) D

(3) I

(4) I

C -

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4) C

-

(1) (2)

(3) (4) A

G -

(1)

(2) C

(3) H

(4) C

-

(1) (2) D

(3) (4) H

DA -

(1) (2)

(3) (4) C

G E

I

(1)

(2)

(3) F

b-

(4)

(1) C (2) (3) A- (4) A

(1) G

(2)

(3) A

(4) G

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

9

CODE F

-

(1) A

(2) A

(3)

A

(4) A

A

-

(1) (2)

(3) (4) C

A 983079A983079

983079B983079

(1) AB AB (2) ABAB

(3) (4) A B

-

(1) (2) -

(3) (4)

C

2011 -

(1) A (2)

(3) (4)

A -

(1)

(2)

(3) E

(4)

H

(1) (2) E (3) (4) F

Aring K C A G(5) (5) 5 (2) -

(1) (2)

(3) B (4) A

-

(1) B (2) I

(3) H (4) F

(1) G

(2)

HC

(3) A

(4) B983079

I DA 17

DA -

(1) G 17 A 165 325

(2) G 17 A 33 33

(3) G 85 A 50 245

(4) G 34 A 245 245

I B B

- -

(1) A H

(2) A -

(3)

(4) A H

C -

(1)

(2) C

(3)

(4)

(A E) -

(A)

(B)

(C) C C A

(D)

(E) I

(1) (B) (C) (D) (2) (A) (D) (E)(3) (B) (C) (E) (4) (A) (C) (D)

7182019 AIPMT2015 Solutions

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A L L E N

10

AIPMT 2 15

(1) = B + F

(2) = + BC + BC

(3) B = + BC + BC

(4) = B

-

(1) D (2)

(3) C (4) I

G I

G G

(1) I C A

(2) G E A C(3) C G

(4) B-

C983079

-

(1)

(2)

(3) E

(4)

G -

(1)

(2)

(3)

(4)

(1) I

(2) D

(3) I

(4) I

C -

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4) C

-

(1) (2)

(3) (4) A

G -

(1)

(2) C

(3) H

(4) C

-

(1) (2) D

(3) (4) H

DA -

(1) (2)

(3) (4) C

G E

I

(1)

(2)

(3) F

b-

(4)

(1) C (2) (3) A- (4) A

(1) G

(2)

(3) A

(4) G

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

10

AIPMT 2 15

(1) = B + F

(2) = + BC + BC

(3) B = + BC + BC

(4) = B

-

(1) D (2)

(3) C (4) I

G I

G G

(1) I C A

(2) G E A C(3) C G

(4) B-

C983079

-

(1)

(2)

(3) E

(4)

G -

(1)

(2)

(3)

(4)

(1) I

(2) D

(3) I

(4) I

C -

(1)

(2)

(3)

(4)

-

(1)

(2)

(3)

(4) C

-

(1) (2)

(3) (4) A

G -

(1)

(2) C

(3) H

(4) C

-

(1) (2) D

(3) (4) H

DA -

(1) (2)

(3) (4) C

G E

I

(1)

(2)

(3) F

b-

(4)

(1) C (2) (3) A- (4) A

(1) G

(2)

(3) A

(4) G

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

11

CODE F

-

(1) G

(2)

(3)

(4)

-

()

() A-II

() A

()

() A

() G2-

() C

() A-I

()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

K -

(1) I (2) A (3) (4)

-

(1) C (2) C

(3) (4) G

A

(1) C (2) E(3) C (4)

I

-

(1) I C

E

(2) I B

E

(3) I

E

(4) I E B G

HI AID

(1)

(2) H -

(3)

(4) B-

H

(1)

(2) -

(3)

(4)

(1) (2)

(3)

(4)

A

(1)

(2)

(3) C

(4)

(1) B (2) E

(3) E (4)

(1) (2)

(3)

(4)

(1) G

(2)

(3)

(4) C

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

13

CODE F

(1) (2) A

(3) C (4) G

I

(1) (2) B

(3) (4)

(1) C

(2) G

(3)

(4)

A

(1)

DA

(2)

DA

(3)

DA

(4)

DA

A

(1)

(2)

(3)

(4)

(1) E

(2) E

(3) E

(4) E

(1) (2) A

(3) C (4) C

(1)

C

(2)

C

(3) B -

A

(4)

(1) I

(2)

-

(3) K

(4) A

-

(1) C-

(2) C -

(3) C-

(4) -

(1)

(2)

(3) H -

(4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

14

AIPMT 2 15

E (1)

(2)

(3)

(4)

(1) H

(2) C

(3) E

(4) H B

A H -

(1)

(2)

(3)

(4) I

(1) C

(2)

(3) C

(4) F

(1) F

(2) F

(3)

(4)

(1) D

(2)

(3) (4) B

(1) A - G

G

(2) C

(3)

(4) A

(A B)

A

B

A

N u m b e r o

f

O r g a n i s m s

Time

(1) B

A

(2) A

B

(3) A

B

(4) B

() ()

() ()

() ()

() ()

() () () ()

(1) () () () ()

(2) () () () ()

(3) () () () ()

(4) () () () ()

(1)

(2) F

(3)

(4) C

A 983079983079

(1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

15

ODE F

(1) (2)m 2

0

(3)m

0

2 (4)m

p0

2

=m0

2 reg

= =

1 =

=

m0

2 ( = 1

)

(3)

5

2

4 6

( )3

( )

(1) 20 (2) 20 (3) 12 (4) 20

D = D amp

=

2 2 1 12 1

-D = - =

2 2 1 1 2 2 1 1

1 1

- -aelig oumlD = =ccedil divideg - g -egrave oslash

THORN38 10

25

- acuteD = =20

(1)

1 = (w)

2 = (w)

(1)

(2) +2 2

(3) +( )

2

(4)

1 = w

amp 2 = w = (w + p2)

= + + f2 21 2 1 2 2

1 =

2 = amp f =

p2

= +2 2

(2) -

() = b 2

b

(1) 2b2 41 (2) 2b2 2+1

(3) 2b2 4+1 (4) 2b2 21

= b 2

= 2b 21

=

= (b 2) (2b 21)

THORN = 2b2 41

(1)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

16

AIPMT 2 15

I 2713 A R

A

12553 T

(1) A5 R3

(2) A3 R5

(3)aelig oumlccedil divideegrave oslash

13

A

13R

53(4)

aelig oumlccedil divideegrave oslash

13

A

53R

13

R micro A13

aelig ouml= ccedil divide

egrave oslash

1 3

A

T

R 27

R 125 THORN RT =

5

3 RA

(1)

I 1

1 A

500

W

(1) 01 (2) 05

(3) 002 (4) 02

A

=

lb l

= =

D

D D

A

=l2

983079

A

l l=10 2 983079

THORN 983079 = 02 = 02

(4)

F

983079l983079

983079983079

I 983079D983079

(1)

lD

(2) l

D

(3) l

2D

(4)

l2D

L = D (2q) = 2Dq

= 2Da

l

qq

D

H O (4) A -

T

(1) (2)

(3) (4)

M

A

H (1)

O P Q

R

P

R

Q I TP T

Q T

R

P Q R

(1) TP gt T

R gt T

Q(2) T

P lt T

R lt T

Q

(3) TP lt T

Q lt T

R(4) T

P gt T

Q gt T

R

F W983079

l micro

1

TN VIBGYOR

(l)P lt (l)R lt (l)QS T

P gt T

R gt T

Q

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

17

CODE F

A 4

8W T

2V

1 V

(1) 40 W (2) 44 W (3) 48 W (4) 32 W

P =1V

= 10 3 V = 10 1V

L R

I =+2

8 R

P

=acute

=+ +

8 2 16

8 R 8 R

P =aelig ouml

acuteccedil divide+egrave oslash

16 1

8 R 4 V

=+4

8 R = 01

THORN R = 32W

H (4)

C 3 H+ (H)

-

K = 9 109

= 2 (P983079 C) = 66 10 34 J

(1) 146 106

(2) 073 106

(3) 30 10

8

(4) 292 106

F H-

n =

2188 106

= 2 = 3

n = 146 106

H (1)

A I

L

X-

R Y- M

O

Y

X

R

I

I

O

I

(1) ( )0micro ˆ ˆB i 2k4 R

I= - p -

p

r

(2) ( )0micro ˆ ˆB i 2k4 R

I= - p +

p

r

(3) ( )0micro ˆ ˆB i 2k4 R

I= p -

p

r

(4) ( )0micro ˆ ˆB i 2k4 R

I= p +

p

r

983079B983079 9830791983079

B1 =mp0I

4 R 90 + q ( )

B1 =

m

p

0I

4 R (

) = B

3

13

I I

2

B 9830792983079

B2 =m0I

4R -( )

983079B983079 = + +r r r r

1 2 3B B B B

THORN r

CB =-m0I

4R

aelig ouml+ccedil divideegrave oslashp

2 =-m

p0I

4 R p + ( 2)

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

18

AIPMT 2 15

W

-B

(1)

l

(2)

l

(3)

l

(4)

l

P =l

THORN P micro l1

(R )

(1)

A C

V

A K

W

(1) T

K

(2) T aelig oumlccedil divideegrave oslash

21 1CV 1

2 K

(3) T

(4) T

K

O

Q = CV

W

=983079NC KC

E =2Q

2C THORN EN =

1

K E

V =Q

C

V =1

K

V

H (3)

T

20

T

-

(1) 100 (2) 120 (3) 140 (4) 80

F

=l

4

2 =l0

3

2

N =l l 0

3

4 2 THORN l0 = 6l = 6(20 ) = 120

H (2) T A

(A2) T

-

(1) 180 2A (2) 90 A

(3) 180 + 2A (4) 180 3A

m =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2Q m = (A2)

(A2) =

d +aelig oumlccedil divideegrave oslash

aelig oumlccedil divideegrave oslash

A

2A

2

THORN (A2) = d +aelig ouml

ccedil divideegrave oslash

A

2

THORN 90 A2 =d + A

2

THORN d = 180 2A (1)

W

Y1

Y2

B

A

Y

(1) NAND (2) AND

(3) NOR (4) OR

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

19

CODE F

1 = A 2 = B

= + = +1 2 A B ( D-983079 )

= A B

H AND H (2)

A C h =1

10

I

10 J

-

(1) 99 J (2) 90 J

(3) 1 J (4) 100 J

F E amp

1

1h =

+ b THORN 1 1

910 1

= THORN b =+ b

2Q

Wb = (F )

2Q9

10= THORN Q

2 = 90 J

H (2)

A l T

-

3V0

2l V0 T

-

(1) 4 l (2)l4

(3)l6

(4) 6 l

VS = E f THORN VS = l l0

3V0 = l l0

(1)

V0 = l l0

2 (2)

(1) 3 (2)

THORN 0 = +l l

0

2

2

THORN l0 = 4lH (1)

A E

T

(C = V ) -

(1)

2E

C (2) 2

2E

C (3) 2

E

C (4)

E

C

ECEC

M =E

C

S

= =2E

CH (1)

A

0 R0 T

R0

0

T

0R

2 T

-

(1)20

1

4(2) 2

02

(3)20

1 2 (4) 20

A C

THORN L = L

THORN 0R = R

2

THORN = 2 0

KE = ( )

2 2

0 0

1

m 2v 2mv2 = (2)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

20

AIPMT 2 15

T -

( 15)

20

T

17 T -

(1) 25 (2) 50

(3) 50 (4) 20

= 172

= 151

F 983079

1 2

1 1 1( 1)

R R

aelig ouml= m - -ccedil divide

egrave oslash

1

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

2

1 1 1(15 1)

20 40

aelig ouml= - =ccedil divide

egrave oslash

amp3

1 2 7(17 1)

20 100

aelig ouml= - =ccedil divideegrave oslash

N1 2 3

1 1 1 1

= + +

THORN1 1 1 7

40 40 100= + -

THORN = 50

H (2)

A A 1

A

B 2

T

W A

-

(1)m+

2 1

1 2

( )

( ) (2)+ m

+1 2

1 2

(1 )

( )

(3)

m

+

1 2

1 2

(1 )

( ) (4)

+ m

+

2 1

1 2

( )

( )

T

A1m

m 1

T

B2

2

F

2 T = 2

T m 1 = 1

THORN - m

=

+

2 1

1 2

( )

F 9830792983079

2 12 2

1 2

T

eacute ugrave- m- = ecirc uacute+euml ucirc

2 1 1 12 2 2

1 2 1 2

T

eacute ugrave eacute ugrave- m + m= - =ecirc uacute ecirc uacute+ +euml ucirc euml ucirc

THORN1 2

1 2

(1 )T

+ m=

+

H (2) A SHM

I 1 2

V1 V2 I

-

(1) 2p2 22 12 21 2

V V (2) 2p +

+

2 21 22 21 2

V V

(3) 2p2 21 22 21 2

V V

(4) 2p +

+

2 21 22 21 2

V V

F SHM

V = w -2 2A

V1 = w -2 21A amp V2 = w -2 2

2A

w =

2 21 22 22 1

V V 2

T

- p=

-

THORN T = 2p

2 22 1

2 21 2

V V

-

-

H (1)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

21

CODE F

A A W

10 1 B 100 S A

N 10 1 T

-

(1) 5 (2) 5 2

(3) 10 2 (4) 0

10 A

B

10

= 1 0 2

B A

45 1

0 0

O

2 2BA 10 10 10 2 = + =

r

OB = 100 45= 50 2

T

A amp B =BA

50 2 50 2

10 2 r =

= 5

H (1)

A W

A B

T

T

A T A -

(1) W

(2) W( )

(3)W( )

(4)

W

B

A Bx

W

dndashx

NB

NA

B

NA() = W()

THORN NA =-W( )

H (3)

T 2700 T

454 10 11 P 1

103 3W

(1) 10 10 2 (2) 12 10 2

(3) 14 10 2 (4) 08 10 2

A

=DP

BV

V

D

=V P

V B

N P = r amp 983079K983079 =1

B

D

= rV

V

(K)

= 103 98 2700 454 10 11

= 1201 10 2

H (2)

T 1

2

1

2 O

e I 1

2

(1)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ = + - e

(2)2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ - e = +

(3)2 2 2 2 2 2 2 2

1 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2+ + e = +

(4) 12

1 +

22

2 e =

12

1 +

22

2

E

K E

= KE

+ E

+ = + + e2 2 2 21 1 2 2 1 1 2 2

1 1 1 1

2 2 2 2

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

22

AIPMT 2 15

K983079

(T)

T

2

= K

3

K

I M

N983079

F = 2

GM

G

T G K

(1) GMK = 4p2 (2) K = G

(3) K =1

G(4) GK = 4p2

T =p p

=2 2

GM

aelig oumln =ccedil divide

egrave oslash

GM

T =p2

GM 32

T2 =p24

GM 3

C

K =p24

GMH (1)

A 10

10 1

F = 01 J

= 20 30 I KE

(1) 450 J (2) 275 J

(3) 250 J (4) 475 J

W = ograve F

W = ograve30

20

01

W = 01eacute ugraveecirc uacuteeuml ucirc

302

20

2

W = 01eacute ugraveecirc uacuteeuml ucirc900 400

2 = 25

F W = K K

THORN 25 = K 1

2 10(10)

2

THORN K = 475

H (4)

A 40

T 250 2

A

(r

= 12 3)

(1) 48 105 N

(2) 24 105 N

(3) 24 10

5

N (4) 48 105 N

B B983079

21P v

2+ r = P0 + 0

2

0

1 p p v

2- = r

P = Pin 0

v = 0in

21F v A

2

= r

F = 24 105

H O (2)

T M 5 M

R 2 R

12 R I

(1) 45 R (2) 75 R

(3) 15 R (4) 25 R

12R

I = 12 R

R 2R

A

= 3R

S =12R3R = 9R

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

23

CODE F

S

1

1 =

2

2

= 5(9R )

= 45R 5

6 = 45R

=45

R6

= 75R

H (2)

A 983079R983079 983079P983079

AC I

983079983079

(1)R

P

(2)aelig oumlccedil divideegrave oslashR

P

(3) P (4)aelig oumlccedil divideegrave oslash

2R

P

P

RR

R amp I

L fX L

R

(P )

AC I =

2V

P R =

V

P V cosZ

eacute ugrave

= fecirc uacuteeuml ucirc

THORN V2 = PR V R

P middotZ Z

2

=

(F )

2

(PR)R P

Z=

2R

P P

Z

aelig ouml= ccedil divideegrave oslash

H (4)

T = gP

V

C

C

()

(1)aelig ouml+ccedil divideegrave oslash

1

3(2)

aelig ouml+ccedil divideegrave oslash

21

(3)aelig ouml+ccedil divideegrave oslash

1

2(4)

aelig ouml+ccedil divideegrave oslash

11

g = 1 +2

H reg

g = 1 +2

H (2)

F

A C

V

210 3 3

410 3 3

210 P4

610 P4

P B C

A

I AB 400 J

BC 100 J

T

AC

(1) 500 J (2) 460 J(3) 300 J (4) 380 J

I ABCA

DU

= 0

Q

= W

QAB

+ QBC

+ QCA

=

400 + 100 + QCA

=1

2 times (2 times 10 3) times 4 times 104

400 + 100 QAC

= 40

QAC

= 460 J

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

24

AIPMT 2 15

I (E) (V) (T)

(1) EV 1T 2 (2) EV 2T 2

(3) E

2

V

1

T

3

(4) EV

2

T

1

A

S micro EV

T

M1L

0T

2 = M

1L

2T

2L

1T

1T

1

M1L

0T

2 = M

L

2T

2 L

T

T

C

+ = = +=

= = + +

2 0 2 2 1

2 2 2(1) 2

= 2

S E

1V

2T

2

S T =S

A

S = times 2

E

V T = E V

2 T

2

H (2)

I - 10 V

+5V

5V

RL

RL

(1)

10V

(2) 5V

(3)

5V

(4) 10V

T P-N

H-

5V

H (3)

T A B C 4 2

1

I 14 N

4 A

B

(1) 6 N (2) 8 N (3) 18 N (4) 2 N

A =

F

M

=14

4 2 1+ + = 2 2

4 2 1

14 N

T 4 amp 2

2 amp 1

F = (2 + 1) = 3(2) = 6N

H (1)

A B C R 15 R

3R W

X

Y VA V

B V

C

T

B

C

AX Y

(1) VA sup1 V

B = V

C(2) V

A = V

B sup1 V

C

(3) VA sup1 V

B sup1 V

C(4) V

A = V

B = V

C

E B amp C =(15R)(3R)

R15R 3R

=+

I V micro R

983079A983079 = B amp C

N B amp C VB = VC

THORN VA = VB = VCH (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

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A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

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A L L E N

25

CODE F

T

C

XX983079

M XX983079 -

X

X983079

(1) 3 2 (2)216

5 (3) 4 2 (4)

211

5

X

X983079

1

2 3

I983079 = I1 + I2 + I3

aelig ouml aelig ouml+ + + +ccedil divide ccedil divide

egrave oslash egrave oslash2 2 2 2 22 2 2

3 3 3

(U )

THORN I983079 = 22 + 22 = 42

H (3)

T

E = A A

983079983079

(1) A e0 2 (2) 4 pe0 A3

(3) e0 A3 (4) 4 pe0 A2

F = E r

r

I

2A(4 )f = p2A()(4 )f = p ( = )

3A4 f = p

N

0

f =

Icirc THORN = fIcirc0

3

0 A4 = p IcircH (2)

T

100C 110C T

40 J I

200C 210C

(1) 168 J (2) 80 J

(3) 40 J (4) 440 J

R micro

THORN 2 1

Q(T T )

micro -

H ( 10C)

S

SQ

= 4 J

H (3)

T P Q

KP KQ KP gt KQ T

( )

( ) T WP WQ () ()

(1) WP = WQ WP = WQ

(2) WP gt WQ WQ gt WP

(3) WP lt WQ WQ lt WP

(4) WP = WQ WP gt WQ

G KP gt KQ

C () 1 = 2 =

2P

P PP Q

2Q QQ

1K

W K2 W W1W K

K 2

= = THORN gt

C () F1 = F2 = F

F

2F 1W W

2K K= THORN micro

S

QPQ P

Q P

KWW W

W K= THORN gt

H (2)

7182019 AIPMT2015 Solutions

httpslidepdfcomreaderfullaipmt2015-solutions 2626

A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)

7182019 AIPMT2015 Solutions

httpslidepdfcomreaderfullaipmt2015-solutions 2626

A L L E N

26

AIPMT 2 15

A 983079983079

I

T

983079V983079 T

I

V

(1) 2

1

(2 ) -(2) 2

1

(2 ) +

(3)1

(2 )(2 ) - +(4) 2

1

xndasha2

a

x + a2

x

I

1 2

V

I (1)

e1 = B1Vl

I (2)

e2 = B2Vl

= B1Vl B2Vl

e = Vl B1 B2

THORN1 2

B Be micro - S1

Br

micro

S1 1

a ax x

2 2

eacute ugraveecirc uacute

e micro -ecirc uacuteecirc uacute- +ecirc uacuteeuml ucirc

THORN( ) ( )

1 1

2x a 2x a

eacute ugravee micro -ecirc uacute

- +ecirc uacuteeuml ucircH O (3)

A

I

(1)1

2 -

(2)1

22 -

(3)1

21

2

-

(4)1

2

2

-

P = F =

THORN K =

B

THORN

=ograve ograve

THORN2

2

= THORN 2

=

12 2 1

2

-aelig ouml= = ccedil divide

egrave oslash

F = =1 2

2

aelig oumlccedil divideegrave oslash

THORN

F2

=

H (4)