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PART-1 : PHYSICS SOLUTION
PAPER-1
SECTIONI
1. Ans. (A)
2. Ans. (B or C)
Sol. F E4 A, E
1, E
2, E
3
A .
3. Ans. (B)
4. Ans. (A)
Sol. B 2
l 60
\E
=2
2 32 30
l = p
5. Ans. (A)
Sol. .
E
= 0 .
6. Ans. (D)Sol. N , .
++
++++
++
++
++
7. Ans. (D)
Sol. f
=
0 0
6l=
e e
I
=0 0
6 3
8 4
l l=
e e
8. Ans. (A)
Sol.3 2
402 3 2 / 3
l= l = = =
ll
l l
20H
2 2
l = = = l
l
Path to Success
ALLENCAREER INSTITUTEKOTA (RAJASTHAN)
TM
CLASSROOM CONTACT PROGRAMME(ACADEMIC SESSION 2014-2015)
JEE (Advanced) # 01
Date : 04 - 05 - 2014TARGET : JEE (Main + Advanced) 2015
ENTHUSIAST COURSE (Phase-I)
HS-1/11
PAPER CODE 0 1 C T 2 1 4 0 0 1
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9. Ans. (A,B,C)
Sol. .
10. Ans. (A,C,D)
11. Ans. (B, D)
Sol. A . A E
.
12. Ans. (A, D)
Sol. B
F F F+ =r r r
\3
F
3
pr=
13. Ans. (C)
14. Ans. (B)15. Ans. (B)
16. Ans. (D)
Sol.0
E
3
a=
\ =2
0
3
a= w
\ = 03
2
p
a
SECTIONIV
1. Ans. 3
Sol.3 7
3 7
3 7
A
B
0
1
2
E s
e
= = N/C \ . B A
V V E e Er q- = - =r r
2. Ans. 5
Sol. A 0 033
34
so un d m ed ium
sound medium source
v vf f f
v v v
- = = - +
B 0 0
35
34
sound mediu m
sound medium source
v vf f f
v v v
+ = = + -
\B = 1 2 035 33
534
f f f- - = =
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3. Ans. 6
Sol. /
2L
= , L . A
, L
,
. (..,)
=
1 1 1
2L 2 2
=
H D D < < , 1
2
D D =
I , = 100 H D = 3 H. H, 2 3
2 6%
100
D D = =
4. Ans. 5
Sol. A () =F 2 1
2 2 2 2= =
() =2 21 1 1 2 1
2 2 2= =
+x1
x2
1+ 2= 8 & =1 2
2
-
5. Ans. 2
Sol. A
=E
A
0.8 102 =q2
2
0.8cm
)45dE
45
F
=
q2 2
2
- q=
q
3
2
8 10 2 2
q= 45-
=38 10
4
2 103 =
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PART-3 : MATHEMATICS SOLUTION
SECTION-I
1. Ans. (C)
() = ( )21
2
2 1 +
+ -
2
2 1 01
02
1 1
2
+ - >
+ >
+
1
,2
2. Ans. (B)
Q
, 1 1 12 . 1
2 2 2
= +
2
1 1 0
2
- =
1 1
2
=
3. Ans. (D)
()
A, () = ( )1 2 2
- p-
\() = ( )1 2 2- - p-
PART2 : CHEMISTRY SOLUTION
SECTION-I
1. Ans (D)
= 2 (10) = 20 . = 2000
D = 1 5/2 (300) = 6250 = D = 8250
2. Ans. (B)
3. Ans. (A)
Sol. = 109, = 103
4. Ans. (D)
5. Ans. (D)
6. Ans. (A)
7. Ans. (C)
8. Ans. (B)9. Ans. (B)
10. Ans. (C, D)
11. Ans. (A,B,D)
12. Ans. (A,B, D)
13. Ans. (B)
14 Ans. (D)
15. Ans. (C)
16. Ans. (D)
SECTION-IV
1. Ans. 2
2. Ans. (1.4) [OMR Ans. 5]
3. Ans. 2
4. Ans. 05. Ans. 2
1 2 2
- p= - y=5 y=5
x=3x= 3 x
(0,4)
graph of y=(x)
(even function)
1 2 2 2
-p p = - -
1 2 ()2
-p= - = -
() .H, (), (), ()
, B () .
4. Ans. (C)
0
()
2
0
1 2 .(1 )(1 2)...(1 2 )2 = + + +
( 1)
1 1. .(2 2 2 ....2)
2 2+
= 1442443
1 1
2
22
2
+-= =
5. Ans. (C)
G 3() () = l
. ..
3(). + () =1
.
4p= ,
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3 1 1 1 4
2 2 2 2
+ = p
1
2
=2
p
6. Ans. (D)
5 3 0
2 .
12 2
12
+ - = -
+ +
5 3 0 1
22( ) 12
-= -
+ +
3
3
5 3 0
.
1
12
- = -
+ +
3
5 3 0
1 1
6 12- = -
+ +
0 2
3
1 1
C 2
=
+ +
\ N C = 0, = 2, .
7. Ans. (C)
l(+ ) =
2+
2....(1) = 0
l(1 + (0)) =
2
(0) ....(2)Q l(1 + ) =
2
( )
= 0
\ (0) = 0 (2)N . (1) .. .
1 . 2 2
+ = + + = = 0
1(1 + (0)) = 0 (0) = 18. Ans. (B)
2 3
2 0
......
2 3
- + - -
2 3
2 0
(1 ) ....
2 3
- - + -=
C 1 = 0 .. = 1
1
2= -l
\ 12
+ =l
9. Ans. (A,D)
L
3
= ,
1 2() 3
3 3
= + + + + =
\ [ ]
() 3. 3
= = .
A, () + () = 2
2 = 2 = 1 1 < 2, .
A, () + () = +
.
10. Ans. (A,B,D)
C () = 1 " I, () I.\ () .
11. Ans. (A,B,D)
1 0 2()
( 1) 2 3
-
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13. Ans. (D)
() = (2)
+
2
2
22
2
1 0 1
1
11 1
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PART-1 : PHYSICS SOLUTION
PAPER-2
SECTIONI
1. Ans. (A)
2. Ans. (D)
Sol.
3. Ans. (A)
Sol.
( )3/ 2
2 2
KE
=
+
rr
4. Ans. (B)
Sol.
5. Ans. (B,C)
Sol. F ()
=
2
0
2 2
0 0
,
3
, 0
2 6
r
r r -
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SECTION-I
1. Ans. (C)
2. Ans. (D)
3. Ans. (C)
4. Ans. (C)
5. Ans. (B, C)6. Ans. (A,B,C)
7. Ans. (B, D)
8. Ans. (A,B,C,D or A,B,C or D)
9. Ans. (A,B,D)
10. Ans. (A,C,D)
11. Ans. (D)
13. Ans. (C)
Sol. 01
v Em
SECTIONII
1. Ans.A-P,R,S,T; B-P,S,T; C-P,R,S,T;
D-P,S,T
SECTIONIII
1. Ans. 003
Sol. E0=
( )2 4
/ 2
l l=
E >> l.
E =( )
2 2
l=
l
02
E E
4
=
l
2. Ans. 100
Sol. 6 6
7 10 10 7T N N-= =
( )
15 7 8B
F N\ = - =
\ = 2 \ A = 100 2
\2 = 100 2 = 100
3. Ans. 008
Sol. =1
22
(82 02) 109 5000 =1
2
1032
64 106= 2
4. Ans. 002
Sol.( )
1
2 1
4
+ l=l ...()
( )2
2 1
4
- l=l ... ()
L l1 l
2=
2= ...() p2 =
2
2
p=
12. Ans. (B)
13. Ans. (C)
SECTION-II
1. Ans. (A) (S); (B) (R,T); (C) (Q,R,T);
(D) (Q,T)
SECTION-III
1. Ans (0.2) [OMR Ans. 200]
2. Ans. (1020) [OMR Ans. 102]
3. Ans. 003
4. Ans. 004
PART2 : CHEMISTRY SOLUTION
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7. Ans. (B,D)
2
2
2 ( 1)()
2 ( 1)
p - -=
+ -
\
0 1
( 1)() 1
( 1)
1 1
p < -
- =
\ 1 () 1
=
() = 1.
8. Ans. (A,C,D)
0
( ) () ()
+ -=
0
() () 3( ) 1 ()
+ + + - -=
0
() 1 3( )
-= + +
= (0) + 32 0
(0 ) (0)( (0)) + - =
Q
() = 1 + 32
() = + 3+ CQ (0) = 1 C = 1\ () = 3+ + 1Q () 0 " \ -
9. Ans. (A,D)
F
.\ D = 0 ( 1)2 4( 1) = 0 = 1 = 5
10. Ans. (C,D)
.
G () :
1
p/4-p/4
C "
- , 0,4 4
p p =
Paragraph for Question 11 to 13
() =()
()
Q () = 1 & 1 .
() .
\ () =3 2( 1)( 2 2 2)
( 1)( 1)
+ + - +- +
.
\ 1
5 5 ()
2 4-
-= = - = 2
\ () = 2(2 1).11. Ans. (B)
() : 2, )12. Ans. (C)
D3 2
1
4 9 13
2(2) 4=
+= =
13. Ans. (B)
( ) 0( ) () 0
- >- =
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(D) G
22
p=
2
2
0 1 3
2
4 5
1 0 1
0 1
1 1 3()
0 3
1 3 5
0 5
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PART-1 : PHYSICS SOLUTION
PAPER-1
SECTION-I
1. Ans. (D)
2. Ans. (D)
Sol. On two sides of wire force is equal and opposite. So, net force on wire is zero.
3. Ans. (D)
Sol. Let a charge flows into earth( )
2
QK a
KQ K 2Q302R 2R 3R
- - = + + = , a = 0
4. Ans. (C)
Sol. uniform Er
with in cavity
5. Ans. (A)
Sol.2K
Q maR
l=
6. Ans. (B)
Sol. Only half of field lines would pass.
7. Ans. (A,B)
8. Ans. (A,C)
Sol.
M
M
K1
K2
60x
x N
1
N2
30
N2cos30 = N
1...(i) & N
2sin30 = Mg...(ii)
M
60
N2
K x2K x
1
(K1+ K
2)x = N
2cos 30...(iii)
3
Mgx
K
9. Ans. (A, B, C)
Sol. V1+ V2= 2V
V' = 2V V2V" = 2V V1V' + V" = 2V
V < 2V 2V V" < 2V
Path to Success
ALLENCAREER INSTITUTEKOTA (RAJASTHAN)
TM
CLASSROOM CONTACT PROGRAMME(ACADEMIC SESSION 2014-2015)
TEST # 02 (Pattern : JEE Advanced)
Date : 18 - 05 - 2014TARGET : JEE (Main + Advanced) 2015
ENTHUSIAST COURSE (Phase-I)
HS-1/12
PAPER CODE 0 1 C T 2 1 4 0 0 5
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V' = 2V 2V < V" 2V < V
0 < V" < V
10. Ans. (A, D)
Sol. 10N would form action reaction pair
11. Ans. (B,C,D)
Sol. At equatorial position direction ofE
ris opposite to direction of p
r
12. Ans. (C)
Sol. E = ( ) ( )0
20
K d1 cos
2 r
ls- q -
l
l
= 25 104 104= 24 104N/C
13. Ans. (A)
Sol. F =( )( )2 0 7
2
K R d25
10 Nr d
-sp l
=
l
l
14. Ans. (B)
Sol. Ft= mg sin q kx cos q; q= 60
at= g sin 60 ( )kx 3g kR
cos60 3 1m 2 4m
= - -
ac= v2/r = 0 released from rest
15. Ans. (B)
Sol. S.E. =
22
2 21 1 1 3 1kR sin kR2 2 2 2
- q - =
= ( )
2 2kR
3 18 -SECTION-IV
1. Ans. 1
Sol. Let charge be present at (x, 0)
9
2 4
9 10 q100
(2 x) 10-
=-
...(i)
3 3tan , sin
4 5q = \ q =Q ...(ii)
q=
q
qand
2
3sin
(3 x) 9q =
- +...(iii)
By (i) (ii) and (iii) x = 1 q = 1 1011C n=1
2. Ans. 8
Sol. Bead will complete the circle if it reaches at B.
3R/2
R / 2
1 1W F.dr km
3R / 2 R / 2
= = - ;21 4k 2W 0 mv v
2 R 3
= - = ;
8kv 8m / s
3R= =
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3. Ans. 8
4. Ans. 1
Sol.dE
F Pdx
= here0
E2 x
l=
pe; 2
0
dE
dx 2 x
l= -
pe
( )2
0
F q 2a2 x
l \ = - pe ; 2
0
qaF
x
l= -
pe5. Ans. 5
Sol.
2 30 62
40
10 2 10
2 10
-
-
p = w
6. Ans. 2
Sol. P
Q
QV
r=
K2Q 3
R 2
\forP'
Q
1 K2Q 3V'
2 R 2r
=
=3 KQ
2 R
By comparing x = 2
PART2 : CHEMISTRY SOLUTION
SECTION-I
1. Ans. (D)
2. Ans. (C)
3. Ans. (C)
4. Ans. (C)
5. Ans. (B)
6. Ans. (A)
7. Ans. (A, D)
8. Ans. (A, C)
9. Ans. (A, B, C, D)
10. Ans. (A, B, C, D)
11. Ans. (C, D)
12. Ans. (B)
13. Ans. (D)
14. Ans. (C)
15. Ans. (B)
SECTIION-IV
1. Ans. (44.5) [OMR Ans. 8]
2. Ans. (0) [OMR Ans. 0]
3. Ans. (36) [OMR Ans. 9]
4. Ans. 4
5. Ans. 1
6. Ans. 4
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PART-3 : MATHEMATICS SOLUTION
SECTION-I
1. Ans. (D)
Put x = 3 + t
t 0
9 t sin t 3lim
tcost+ - -
( )t 01 9 t 9 sin t
limcos t tt 9 t 3
+ - -
+ +
1 51 1
6 6
= - = -
2. Ans. (A)
( ) 1x cos cos x2
-p= -
( ) ( ) 7 10 4 10 102 2p p= - p - = -
( ) ( )2
1' x sin x
1 cos x= + -
-'(10) = 1
\(10) + '(10) =7
112
p-
3. Ans. (C)
g"(y) =( )
( )( )3
" x
' x-
Now, if y = 1 x = 0
\g"(1)( )( )
3
"(0)
' 0
-=
Now, '(x) = ex
"(x) = ex
\'(0) = 1 & "(0) = 1\g"(1) = 1
4. Ans. (C)
( )( ) ( )3 3 2d x ' x .3xdx
=
Now, ( )( ) ( ) ( )2
3 3 4 5
2
dx " x .9x ' x .6x
dx= +
( ) ( )6 4 39 x .x 9 x .6x= +\k = 9, a = 4, b = 6, ; p = 6 & c = 3\(a + b + c + p + k) = 28
5. Ans. (C)
( )1sin x
2
1 x e .
1 x
-
=-
\x = 0 y = 1&
( ) ( ) ( ) ( )
1 13
sin x sin x 2 22
1 1' x e . e . 1 x . 2x
21 x
- - - = + - - -
-
= 1 + 0 = 1\Equation of tangent is y 1 = x 0y = x + 1
6. Ans. (A)
Given curve is a homogenous equation
Hence
( )
2
2
1,1
d y0
dx
=
7. Ans. (A,B)
Put x3/2
= t
\3/ 2
1
3 / 23 2
2 dt 2 xI sin c
3 3 aa t
- = = + -
8. Ans. (B,C)
Put 1 x z+ = dx = 2(z1)dz
\
( )8 6 7
2 z 1 1 1
dz 2 cz 6.z 7z
-
= + + -
( ) ( )7 6
2 1c
7 1 x 3 1 x= - +
+ +
\k1= 7 & k2= 69. Ans. (A,C,D)
( ) ( )1 ; x n
x where n I0 ; x n
= p=
p
10. Ans. (B,C)(1 + 3x + 2x2)6= a0+ a1x + a2x
2+ ......+a12x
12
\coefficient of x12= 26
coefficient of x11
=6C5.2
5.3 = 9.2
6
\(B) is correct.Now, a0+ a1+ a2+......+a12= 6
6
a0 a1+ a2......+a12= 0
\a0+ a2+ ....+a12=66
2& a1+ a3+...+a11=
66
2
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Now,
6
2r 6 6r 0
612
a6 3
a 2.2 2= = =
\(C) is correct.
&
6
6 62r 1r 1
612
a6 3
a 2.2 2
-= = =
11. Ans. (A,B,C)
15C2r>
1
215
C2r+1
( ) ( ) ( ) ( )15! 1 15!
2r ! 15 2r ! 2 2r 1 ! 19 2r !>
- + -
4r + 2 > 15 2r 13
r r 2
6
> >
\r =5,6,7 but will not hold when r = 8Paragraph for Question 12 & 13
P(x) = (x3 x) Q(x) + (ax
2+ bx + c)
where R(x) = ax2+ bx + c
\P(0) = c = 2P(1) = a + b + c = 4 a + b = 2P(1) = a b + c = 2 a b = 0\a = 1 & b = 1\R(x) = x2+ x + 2
12. Ans. (C)
Now, ( ) ( )
2 2
3
x x 2 x x 2dx dx
x x 1 x 1 x x
+ + + +=
- + -
3
2
dx dx2
1x 1x 1
x
= +- -
( ) 21
n x 1 n 1 cx
= - + - +
l l
( ) ( )2
2
x 1 x 1n c
x
- + = +
l
\ ( ) ( ) ( )
2
2
x 1 . x 1 x
x
- +=
13. Ans. (A)
Now, (R(x) x)10
= (2 + x2)10
\Coefficient of x3in (2 + x2)10is 0
Paragraph for Question 14 & 15
(x) = (1).x2+ x '(x) + "(x)
& (x) = x2+ xg'(1) + g"(2)
'(x) = 2x + g'(1) & "(x) = 2\g(x) = (1 + g'(1) + g"(2)). x2+ x(2x + g'(1))+2Now, g'(x) = (1+ g'(1) + g"(2)). 2x + 4x + g'(1)Now, g'(1) = 2 + 2g'(1) + 2g"(2) + 4 + g'(1)
g"(2) + g'(1) = 3Also, g"(x) = (1 + g'(1) + g"(2))2 + 4g"(2) + 2g'(1) + 6 = 0\g'(1) = 3 & g"(2) = 0\g(x) = 2 3x & (x) = x2 3x
14. Ans. (A)
3 2
6 4 5
2
2 32 3x x xdx dx
1 34x x 3x 4x x
--=
- + - +
22 4x 3x 1 c
x+ - +
15. Ans. (C)
Now, h(x) = (sinx)|x(x3)| + sin 5| x | x 7+ -\h(x) is non differentiable at x = 0,3,7\3 points
SECTION IV
1. Ans. 1
( )2
24
2 2
1 cos xsin xdx dxcos x cos x
-= 2 2sec xdx cos xdx 2 dx= + -
1 sin 2xtan x x 2x c
2 2
= + + - +
\ ( )sin 2x 3x
g x4 2
= -
\1
g 12 8 8
p p - -
\1
8 18 8 8
p p + - =
2. Ans. 7
R.H.D of |3 x| at x = 3 is 1.
Now, ( )
3
x 0
xlim 1
a x tan x bx=
+ -
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3
3x 05
xlim 1
x 2a x x x bx
3 15
=
+ + + -
Now, if limit is existent\b = 1
& 3 1 a 9a
= =
\a 2b = 73. Ans. 9
( ) ( ) sin x sin xx x cos x 1 e dx xe c= + = +Now, (0) = 0 = 0 + c c = 0\(x) = xesinx
Now,
g(x) = ( )cos x cosxe x sin x 1 dx xe c- = - +Now, g(0) = 0 = c c = 0\g(x) = xecosx
Now, (x) + g(x) = 0 esinx= ecosx& x=0tanx = 1 & x = 0\9 solution
4. Ans. 2
( ) ( ) x
e . ' x dx 2xdx= e(x) = x2 + c (x) = ln(x2+ c)
Now, '(x) = 2
1
x c+ .2x
( )
2' 1 1
1 c= =
+c = 1(x) = ln(x2+ 1)
Now, (x) = '(x) ln(x2+ 1) = 22x
x 1+
ln(x +1)2
Hence 2 solutions.5. Ans. 5
(0, /2)p
1 p 2 p 3p 4pp-2 p1
(x) is non derivable at x =1,0,p1 or 2p,3p6. Ans. 9
n10 10r
nr 1 r 1r 1
C n r 1r. r.
C r= =-
- +=
\ ( )10
r 1
n r 1 5n=
- + == (n + 1)10 55 = 5n
5n = 45 n = 9
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1. Ans. (1)
Sol.kq
10R
=
So, For symmetrical point P.
P
kqV
2 2R=
P2RP 2.5 volt=
2. Ans. (1)
Sol. The potential at centre of sphere in which qcharge is uniformly distributed throughout thevolume is -
c0
1 3qV
4 2R=
pe
By smmetry the potential at centre due to halfsphere will be half of the complete sphere.
\ c 0 0
1 3q / 2 1 3Q q
Q4 2R 4 2R 2
= = = pe pe Q
3. Ans. (2)
Sol. xv
E 4xx
= - = -
; y
vE 3
y
= - = +
x y E E i E j 4xi 3j 3jN / C= + = - + =
r
4. Ans. (2)
5. Ans. (2)
Sol. Electric field at each point on the surface of ring
due to dipole is 3kpE R=
in direction opposite to the dipole moment.(figure below)
R
E
p
Hence net force on ring is3
kpQF QE
R= =
SOLUTION
Path to Success
ALLENCAREER INSTITUTEKOTA (RAJASTHAN)
TM
CLASSROOM CONTACT PROGRAMME(ACADEMIC SESSION 2014-2015)
TEST # 02 (Pattern : JEE-Main)
Date : 18 - 05 - 2014TARGET : JEE (Main + Advanced) 2015
ENTHUSIAST COURSE (Phase-I)
PAPER CODE 0 1 C T 2 1 4 0 0 6
PAPER-2
6. Ans. (4)
7. Ans. (1)
Sol. Velocity of A w.r.t. plank = V
Velocity of B w.r.t. plank = 3V.
L LT
3V 4V= =
+
Their relative displacements w.r.t. plank are
3L L&4 4
.
8. Ans. (2)
Sol.
- ...(i)
..(ii)
Solving equation (i) & (ii) h = 4R9. Ans. (3)
Sol.
9 6kq 9 10 9 10V
CB 27
- = =
81 10003000Volt
27
= =
10. Ans. (2)
Sol.KQe KQe
R 9R
+- 2
KQe KQe 1mV
R 9R 2
-= + +
22KQe 2KQe 1 mV9R R 2
- + =
2
0
16 eQ 1. mV
4 9R 2=
pe
0
8eQV
9 mR =
pe
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11. Ans. (4)
Sol. x y E E i E j= +
r, DV = E
xDx E
yDy
for A and B
16 4 = Ex(2 2) E
y(2 2)
Ex= 3V/m
for B and C
12 16 = Ex(2 (2)} E
y(4 2)
Ey= 4V/m.
( ) E 3i 4 j V / m\ = -r
12. Ans. (1)
Sol. Work done by field
W = DU = UAUB= (e)VA(e)VB
1.28 10
18
= 1.6 10
19
(VBVA)
VBVA= 8 volt VEVD= VAVB= 8 volt
13. Ans. (2)
14. Ans. (2)
Sol. q =2 2
0 00
rE.ds 4 r 4 r 6
a = p = p a =
15. Ans. (1)
Sol.
( )
( ) ( )
9 99 10 1 2 103V.
3 3 3
- + =
16. Ans. (4)
Sol.45452p 2p
= 4p
2p
17. Ans. (1)
Sol. Direction of electric field is perpendicular tosurface of circular base, so work done byexternal agent from B to C is zero.
18. Ans. (1)
Sol. For r < a, E r For b < r < c, E = 0
For a < r < b,2
1E
r For 2
1c r, E
r<
19. Ans. (3)
Sol. Vball = 0
KX Q0
r R
K+ =
Qrx
R = -
Potential difference Vs Vb=KQ Kx
R R+
because potential difference depend only on
charge on inner surface after electrostatic
condition is reached after grounding.
s b KQ rV V 1R R
- = -
20. Ans. (2)
Sol.2K
Er
l=
20
1
RV 2k n
R
= l
l
21. Ans. (3)
Sol.1 1 1
KQ ......r 2r 4r
= + + +
KQ 11r 12
=-
= 2KQr
22. Ans. (4)
Sol. Flux =inside
0
q
23. Ans. (1)
24. Ans. (3)
25. Ans. (2)
26. Ans. (4)
Sol. dV E.dr= -
0
V 2
0V 0
dV dZ2
s= -
V V0= 0
Z
2
s
V = V00
Z
2
s
27. Ans. (4)
Sol.dV
Edx
= -
28. Ans. (1)
Sol. Total charge on ring Q = l = l p l
Then VP=
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29. Ans. (4)
Sol. V0 VA= 400 1
2 2 102= 4 2
V0 VB= 400 1
2 3 102= 6 2
VA VB= 2 2
30. Ans. (1)Sol. W = q DV = q0(VQ VP)
= q0(VP VQ) = q02Klln2r
r
= 2Klq0ln1
2
31. Ans. (3)
32. Ans. (3)
33. Ans. (4)
34. Ans. (3)35. Ans. (2)
36. Ans. (4)
37. Ans. (3)
38. Ans. (2)
39. Ans. (1)
40. Ans. (2)
41. Ans. (4)
42. Ans. (4)
43. Ans. (4)
44. Ans. (3)
45. Ans. (2)
46. Ans. (1)
47. Ans. (3)
48. Ans. (1)
POCl3+ 3H
2O H
3PO
4so oxidation state of
P = +5
49. Ans. (1)
50. Ans. (1)
51. Ans. (3)
52. Ans. (3)
53. Ans. (4)
54. Ans. (4)
55. Ans. (2)
56. Ans. (4)
57. Ans. (3)
58. Ans. (4)
59. Ans. (4)
60. Ans. (3)
61. Ans. (2)
3 3
3(x 2) 1dx dx
(x 2) (x 2)
+-
+ +
2 2
3 1 (6x 11)C
x 2 2(x 2) 2(x 2)
- += + = - +
+ + +
62. Ans. (3)
2 2
(2x 2) dx2
x 2x 2 x 2x 2
+-
+ + + +
= ln(x2+ 2x + 2)2
dx2
(x 1) 1-
+ += ln(x2+ 2x + 2) 2tan1(x + 1) + C
63. Ans. (2)(x) is continuous
x 0 x 0lim (x) lim (x) (0)
- + = = 0 = p
(x) is differentiable
x 0 x 0lim '(x) lim '(x)
+ - = k = 2
64. Ans. (3)
33 x 0x 0
5(sinx x)1 5sinx 1 5limlim 1 .1 5x (1 5x).xx 6e e e
-+ - - + + = =
65. Ans. (2)
At t = 1, x = 3t2 2t dx
6t 2dt
= -
y = t3 12t 2dy 3t 12
dt= -
\2dy 3t 12
dx 6t 2
-=
-
dy
dxat x = 1 is
9
4-
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66. Ans. (4)
1 1
2
tan x.cot xdx
1 x
- -
+put tan1x = t
2
1dt dt
1 x=
+
32 tt. t dt t C
2 4 3
p p - = - +
1 31 2 (tan x)(tan x) C
4 3
--p= - +
67. Ans. (1)
xe (cos(sin x) cosx sin(sin x))dx-use x xe ((x) '(x))dx e (x) C+ = += excos(sinx) + C\ (x) = excos(sinx)(p) = ep
68. Ans. (1)
1y sin 3x
4=
dy 3cos3x
dx 4=
x3
dy 3
dx 4p= = -
69. Ans. (3)
2
1[x 1], 1 x
2(x)
1x 1, x 3
2
- -
= + <
\ (x) is discontinuous at x = 0,1
2
Sum of values =1
2
70. Ans. (4)
put log (x) = t
1. '(x)dx dt
(x)=
2 2t log (x)tdt C C
2 2= + = +
71. Ans. (3)
1/ 2
2 1/ 2
3 2
11
(x x) xdx dx
x x
- - =
put1
1 t
x
- = 21
dx dtx
=
3 / 2
3 / 21/ 2
x 12
t xt dt C C
3 32
- = + = +
72. Ans. (2)
xx e [cos 2x 2 sin 2x]e cos2xdx C
5
+= +
\ (x) = cos 2x 2 sin 2x
5
+
\ range is1 1
,5 5
-
73. Ans. (2)
2 2
2 2x 1 x 1
x( x 1) (x x 1)lim (x) lim
( x 1) ( x 1) - + +
=- +
=9
4
(x) is continuous k =9
4
74. Ans. (1)
3x yy e +=
\dy
dx=
3x y 2 dye 3xdx
+ +
2dy(1 y) 3yxdx
- = 2dy 3x y
dx 1 y=
-75. Ans. (1)
We get only even power of x\ a
1= a
3= a
5= ....... = a
99= 0
\50
2r 1r 1
a 0-=
=76. Ans. (3)
dy
dx=
2
1 1 ' .
x x
-
2
2
1 1sin
x x
- =
3x
dy 3.
dx 3 2 2 3=p
p p= - = -
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77. Ans. (4)
Middle term has greatest binomial coefficient
\m
40 m m 40m i m i
20i 02
C C . C+ -+
=
= 40 m 40 m
m m20
2
C C+ ++
=
\m
20 m2
+ =
m = 4078. Ans. (4)
Put
2xe
e t =
2x2e xe .e .2xdx dt
=
\2xe1 1dt e C
2 2
= +79. Ans. (4)
'(x) = log(1 + x) x
2x 0
(x)lim
x0
0
form
x 0
'(x)lim
2xL-Hpital
x 0
log(1 x) xlim 0
2x+ -
=
80. Ans. (2)
(x) is non-differentiable
where sinx + cosx = 0
3 7
x ,4 4
p p=
81. Ans. (3)
1 2
tan x cot xI I dx
1 cot x 1 tan x
+ = + - -
2
tan x 1 dxtan x 1 tan x(tan x 1)
= - - -
2tan x tan x 1dx
tanx
+ +=
11 dx
sinxcosx
= +
2 cosec2xdx dx= +
= x n cosec2x cot 2x C+ - +l
82. Ans. (3)
'(x) = ex(cosx sinx)
''(x) = ex(2sinx)
'''(x) = ex(2sinx 2cosx)
'''(x) = 4excosx = 4(x)
\ 8(x) = 16excosx = 16(x)
83. Ans. (1)
2 0 1/2 1 3
\ non differentiable at 5 points.84. Ans. (2)
2
4
x 2dx
x 4
-
+
2
2
2
21
x dx4
xx
-
+
2
2
21
x dx2
x 4x
-
+ -
put2
xx
+
= t
2
dt
t 4-
1 t 2log C
4 t 2- ++
=2
2
1 x 2x 2log C
4 x 2x 2- + ++ +
85. Ans. (3)
I1= 49, I
2= 50, I
3= 50, I
4= 50
\ I1+ I
2+ I
3+ I
4= 199
86. Ans. (4)
(x) = 1 + xnor (x) = 1 xn
QP(3) = 10 (x) = 1 + x
2
2(x)dx (1 x )dx= + 3x
x C3
= + +
g(x) =3
x C3
+ + Q4
g(1) C 03
= =
g(3) =33
3 123
+ =
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87. Ans. (1)
P =
40 n
40n
1C .
2
-
......(i)
( )n
39 n10 9 9
n 9
12 P C . 2 .
2
- =
......(ii)
\ 210
40
Cn2n40
=39
Cn
235118n
40381 19nn
39n
C2
C-=
\ n = 20 m = 20, q = 1988. Ans. (4)
n
1 1( n) 2x 2 | x | 2x 2 | x |
n nlim
12x 2 | x |
n
- - - - +
- +
2
n n
4x 1( n)
| x |n nlim lim , x 0
1 x2x 2 | x |
n
- - +
=
- +
at x = 0 value is 089. Ans. (2)
Let1
(x 1)(x 2).....(x 10)+ + +
3 101 2 a aa a
.....x 1 x 2 x 3 x 10= + + + +
+ + + +
put x = 1 \9
01
C1a
9! 9!= =
x = 29
12
1 Ca
8!1! 9!
-= = -
M M
x = 10
9
910 C1a
9! 9!= - = -
\10
i 1i
i 1
( 1) a+
=
- = a1 a2+ a3...... a109 9 9 9
0 1 9C C ..... C 2 4
9! 9! 2835
+ + += = =
90. Ans. (3)
(sin 50x) (sin 20x) dx= sin(30x 20x) sin20xdx+
= sin 20xcos30x sin 20xdxsin30xcos20x sin 20xdx+
=3 / 2sin30x (sin20x)
30
1/ 2sin 30x 3. (sin20x) .20cos20xdx
30 2-
(sin30x)(cos2x) sin 20xdx+
\ a = 30, b = 20,
3p
2=
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PART-1 : PHYSICS SOLUTION
PAPER-1
Path to Success
ALLENCAREER INSTITUTEKOTA (RAJASTHAN)
TM
CLASSROOM CONTACT PROGRAMME(ACADEMIC SESSION 2014-2015)
Date : 08 - 06 - 2014TARGET : JEE (Main + Advanced) 2015
ENTHUSIAST COURSE (Phase-I)
HS-1/11
PAPER CODE 0 1 C T 2 1 4 0 0 9
SECTION-I
1. Ans. (C)
Sol. 10
E 2
s=
e
r
1
2
3
4
x
y
x
x
s
2 3
0
E 0, E 2
s= = +
e
r r
4
0
E
2
s= -
e
r
2. Ans. (D)
Sol.
2QJ
t= ( )
221 1 1 1
2
2 2 2 2
J Q2 2 4 32
J Q
t= = =
t
3. Ans. (B)
Sol. B
3v0V0
Vcm
t
4. Ans. (D)
Sol. B
N C2
2
= P ; =
5. Ans. (A)
Sol.
O
1 /2 2
( )2 2 2 20 1 1 1 2 2 2L mu gt m gt ut mugt mugt mugt k= - = - = -
6. Ans. (A, B, C)
Sol.
2M
2R/3R/3
M
2
2
G2M
R= 2M w2
R
3
w= 33GM
R
KM
=1
2M(w 2R/3)2
7. Ans. (B,C)
8. Ans. (A, C, D)
Sol. D
S
9. Ans. (A, B, C, D or C,D)
Sol. C
0
Q =
. F
.
I
.
10. Ans. (A, C, D)
Sol. ll
3l
TEST # 03 (Pattern : JEE-Advanced)
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2KE 2 ( R)
l =
r
11. Ans. (C,D)
12. Ans. (C)
13. Ans. (D)
Sol. (12 & 13)
L &
w A
L
= L
0 = R 2
MR
2
w
w=2
MR... ()
E
1
22=
1
22+
1
2Iw2
... ()
=M
M 2+
, w= M
2MR M 2+
14. Ans. (A)
Sol. 0= 2 ... (1)
2
00
12
= +
l...(2)
15. Ans. (A)
Sol. V
1
4
=0
2
0
2
p
SECTION-IV
1. Ans. 4
Sol. ( )1/ 2
2 2
0
R 8
s + - e
2. Ans. 5
Sol.
2 F ( ) 2 ( ) (2 )
= + l + + l + + l
l
l
rl l l l l l l
l l l
3. Ans. 3 or 4
Sol. ( ) ( )2 21 1 2 22 2
MR MR5 5
w = w
2 2
1 2
1 2
R R
T T= R2=
1/ 2
221
1
TR
T
4. Ans. 6
Sol.q
R
a a qq
F2F1 qq0
F1= F2= ( )
0
2 2
R+F = 2F
1q
F 0 R
R 2= =
2
2
R2
F0
R=
2
5. Ans. (D)
I = + = + = -11
3 / 2 3/ 2
00
2 21 (1 ) (2 1)
3 3
2(2 2 1)
3= -
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6. Ans. (A,B,C)
(A) ()=
+
x sin x x [0,1]
x sin x x [ 1, 0)
+ =
- - -() (1) = (1)
() - = 0
(B) ( ) -
+ = - -
=
l2
2
( 1) ( ) 1,0
1 1
0 1,0
() = 0(C) () = + = + ()
0 x I([ x] [ x])
1 x J
= - + - -
/\ D = 1, 0
(D) () R .7. Ans. (A,D)
(A)cosx
0
dxI
1 (sin x)
p
=+
/ 2
cos x cos x
0
1 1dx
1 (sin x) 1 (sin x)
p
-
= + + +
(B)p p
= =+
/ 2 5
5 5
0
I
4
(C)
+
- +
2
2
0
11
1
1
=1
0
1
- -
2 2
p p= + = p
(D) ( )p p
=l l/ 2
0
2 2
8. Ans. (B,C)T () = + ( 0)
1() =x b
a
-
9. Ans . (Bonus)
(A) {
3 2
I II
. = 142432 2tan x tan x
x. dx2 2
= -
21 (x tan x (tan x x)) C2
= - - +
21 (x sec x tan x ) C2
= - +
\ () = 2 & () = \ A
(B) = = 0 & = 1
\ = p, 0, p, 2p\ 4 .
(C) () = ()
(D) = 2 2 + 1 = 1
.
10. Ans. (C,D)
() =
+ = 32 + 3 = 32 32 = .2(3 )
g ' 3g 3 x
=-
I n | g(x) | 3 n | 3 x | C= - - +l lQ () = 1 = 0
3
1g(x)
| x 3 |=
-
11. Ans. (C,D)
= 2 5 7 13
\ N = 3 3 3 3 = 81Paragraph for Question 12 & 13
() = ( ) - -
0 0
( ) .
x x
0 0
(x) (t ) cos tdt cos t dt= - () = ()
'(x)
cosx
(x ) 1
=
-I ... ,
l()1 = + C
N, (0) = 0
= 0 () 1 =
() = 1
.
B (0) = 0 () = 1 .12. Ans. (D)
N () .
A () = 0
= 1 = 0 = 0, p, 2p
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A () = 0 a & b\ (a) = (b)\ U R () = 0
(a, b)B () -.
\ (D) .13. Ans. (B)
\ R () 1
1 e, 1e
- - \ 2 .
Paragraph for Question 14 & 15
"() = 2
\ () = ( 2)2+ \ () = 2( 2)Q (3) = 24 \ = 12\ () = 12( 2)2 4(Q = 4)\ () = 43 242+ 44 24\ () = 4 83+ 222 24 ((0) = 0)
14. Ans. (D)
( ) ( )
1
0 - -1
3
0
16 48 28= + =15. Ans. (B)
= 2 0
= 2 : = 8
\E : + 8 = 0SECTION-IV
1. Ans. 8I
13
(12 2) .. 2122
A 13 > < 7N = 210+ 28+ 26+ ..... + 20
= 1365
\ N = 1365 = 3 5 7 13\ D 5 8
2. Ans. 7
( ) ( )4 3
1
1 5
-+ = 12 5 = 7
Q .
\ (1) = 5 & (4) = 33. Ans. 2
S = 12C2= 66
T = 13C3 6 = 286 6 = 280
D = 12C2 12 = 54\ T + D + S = 400T D S = 160
\ T D S
2T D S
+ + = - - 4. Ans. 6
( )1
0
2= =
1
2
N, () = xba
\a
0
(x)dx 2ab=
1 a
0 1
(x)dx (x)dx+ = 2
= 6
5. Ans. 2
1
3
1
( ) ()-
-
= - + - - -1
3 3
0
(( ) () ( ) ( )
1
3 3 3 3
0
(x)(x k 3xk(x k) x k 3xk(x k))dx= + + + + - - -
1
3 2
0
(x )(2 x 6xk )dx 64= + = 2.3+ 6.2. = 643= 8 = 2
6. Ans. 1
( )2
1
-
0 1 2
3 4
1 0 1
x dx x dx 1.dx-
= + + 0 1
4 5
1 0
x x1
4 5-
= + + 1 1 1914 5 20
= - + + =
\ 20 19 = 1
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PART-1 : PHYSICS SOLUTION
PAPER-2
SECTIONI
1. Ans. (A,B,C,D)
2 . Ans. (A,B,C,D)
Sol.
=0 02 2
3
=
+ +
2 2
1 1
2 2m = =
22 00
1
2 2 4 =
(C)0 0
2 2=
(D) A = 0
3. Ans. (A, B, C)4. Ans. (A, B, C)
5. Ans. (B, C, D)
6. Ans. (B, C)
7. Ans. (A,B,C)
Sol. I
8. Ans. (A,C,D)
9. Ans. (D)
10. Ans. (B)
Sol. K
=2
C
12
2 = ( )
2
0 0 2 1 22 2
-
=
2 2
0 0 1 22 2 4
=
11. Ans. (B)
Sol.
a- .
SECTIONII
1. Ans. (A) (P,Q, T) ; (B) (Q,R,T) ; (C) (Q) ; (D) (Q, T)
CLASSROOM CONTACT PROGRAMME(ACADEMIC SESSION 2014-2015)
TEST # 03 (Pattern : JEE-Advanced)
Date : 08 - 06 - 2014TARGET : JEE (Main + Advanced) 2015
ENTHUSIAST COURSE (Phase-I)
PAPER CODE 0 1 C T 2 1 4 0 1 0
Path to Success
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SECTIONIII
1. Ans. 002
Sol.2
l =
mg
2kl
hq
hF =2
l -
=
2
p
2. Ans. 020
3. Ans. 000
Sol. F & . 0E r E r = ^r rr r . 0E Af= =
rr
4. Ans. 004Sol. F LC
= 1+
2
& = 1
= 2
1
1
2
1
4=
= 1 =
2
4
=
SECTIONIV1. Ans. 3
Sol.
3 / 2
2
1
10500 1
42000 8
= =
2= 3
2. Ans. 7
Sol. 0 322
4 1 1G
3 18
2
pr - - 3. Ans. 6
Sol. =
4. Ans. 5
Sol. 0R
kQ
x
kq=+
= x
qR
.
q
Q
R
x
++
+
dt
dQ=
dt
dx
x
qR2 =
3 310 2 10
2 2
- -
= 0.5 106
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PART-3 : MATHEMATICS SOLUTION
SECTION-I
1. Ans.(A, B, C)
2. Ans. (B,C)
3. Ans. (A)
4. Ans. (A, B, D)
5. Ans. (B, C)
6. Ans. (B)
7. Ans. (A,B,C,D)
8. Ans. (A,B,C)
9. Ans. (D)
10. Ans. (D)
11. Ans. (B)
SECTION-II
1. Ans. (A)
(Q,S);(B)
(R,S);(C)
(P,T);
(D)(T)
PART2 : CHEMISTRY SOLUTION
SECTION-I
1. Ans. (A,C)
( ) . 1
1 1
1
+= =
+ +++
+ 2+ = (1 + ) ...(1) = 0, 2+ 2 = 0 2\ = 0, (1) ,
( )
2 . 1 . 0
+ - + - - + =
= = 0 ( )1
02
=
2. Ans. (A,B,D)
B I.. (C)
A,B,D .
3. Ans. (A,D) & ,
22 3 13 3 4
2 1 2 2 2 9 9
C C . C C . C
= - -
= 231 234 18 = 15
A : B ,
( ) ( ) ( ) ( )3 3 3 6
8,8, 4 , 7, 7, 6 , 6, 6, 8 , 7,8, 5 ,
\ = 15.
SECTION-III
1. Ans. 075
2. Ans. 9 1022
OMR Ans. 922 or 036 or 1983. Ans. 002
4. Ans. 004
SECTION-IV
1. Ans. (2400)
OMR Ans. 6
2. Ans.(16)
OMR Ans. 7
3. Ans. 6
4. Ans. 1
4. Ans. (B,C,D)
G, ( + ) = (). () ...(1)
= = 0 (0) = 1 (Q(0) 0) = (1)
\(1) (). () = (0) = 1
( )( )1
- = ...(2)
B (2), F() .
(B)
2014 0 2014
2013 2013 0
F() F() F()- -
= +
2014 2013 2014
2013 0 0
F() F() F()-
- = 0 2013
2013 0
F() F()-
=
Q
(C) L
2013
2013
F()I ()-
= ...(1)
( )
2013
2013
F()I
-=
- (QF() = F())
( )( )
22013
2
2013
I
1 -=
+ ...(2)
(1) + (2)
2013
2013
2I 1.
-
= I = 2013
(D) F() F() = 0
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5. Ans.(C,D)
G
( )( )1 1
2
2 2 0 1 0
1 / 1 1
1 21
=
= = = ++ +
l
12 2
2= =l l
6. Ans. (A,B,C,D)
( ) ( )/ 2 1
0
2 1 2 1
p
+
+ - -- =
/ 2
0
22.
p
= / 2
0
22 0
2
p = =
\+1= 1= 2= 3=......../ 2
0
2
p p= =,
( )2 2/ 2 1 2
0
1
p
+
+ -- =
( )/ 22
0
2 1 .
p +=
( )/ 2 1
0
2 1
p
++= =
7. Ans. (A,B,D)
(A) () 0,2
,
.
(B) Q() = ( 1)2+ 2
\ () = (1,2), () (1,3).
(C) L ( ) ( ) 1 5 4
p= + - + p
0,1 () 0,1.A, (0) = 5 (1) = 4
\(0). (1) < 0, I... () = 0 (0,1).
(D) C ( )1
2 3
0
I = + + +
12 3 4
0
I 2 3 4 2 3 4
= + + + = + + +
12 6 4 30
12
+ + += =
\() (0,1).8. Ans. (A,B,D)
P
L1
L2
I L1
L2
L1 L
2.
\
=C
2.C
2=
( )2
1
2
-
A,( )
2
1100,225, 784
2
-=
= 5,6,8
.
Paragraph for Question 9 to 11
2() = (())+ (())",
= 1
\ 2() = () + 5() = 5
9. Ans. (D)
Q = 5 =
2
\1=
2 5l5 = .2
2.l5 = .2 2
5
=l
1
5= .
2
22
52
5 .5
=
l
l
1
22
2 52
5 . 5 .5
= =
l
l
5
2
2 25 . 5
= l
2 5
2
=
l
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10. Ans. (D)
() = (5) () = (5).5l5.
Q 5 (0,)
(0,), () -
5= (2 + 1) 2
p( I)
. C () 1,1.
11. Ans. (A)
2
1 2
() 5 5
() (1 ) 5 5 5 5-= =
+ - + +
( )21
. 5 5 C2 5
= + +ll
( )( )
1. 5 2 C
2 5= + +l
l
SECTION II
1. Ans. (A)(T); (B)(P); (C)(Bonus);
(D)
(R)
(A) G = 5 ...(1)
= - =
, + + = 0
= - .
() . = ()
(B) 2 = 3
2 + ...(1)
1 3
2 6
= = =
2= 4 ...(2)
2
2
2 4 = = =
\1
2= 1
2
2
61 6
= - = -
(2) 4 = 6
= 0 \ = 0 = 0
1
2 .
.
(C) () = (
2
1).
2
> 0 " 0,p (2 1) > 0 > 1 < 1.
\ = 2,3( = 1 )
(D) (x) = min.{ 2 x2,2 ,
2+ 1
\\\\\\\\\\\\\\\\\\\\\\\
\\\\\\\\\\\\\\\
\
\\\\\\\\\\\\\
\
y = 2x2 (0,1)
\\\\\\\\
(2,0)( 2,0)
R(1,1)
y=1+x2(0,2)
P
y=2x
() - ,, ..
3 .
SECTION-III
1. Ans. 078
() = 9 2 l> 0 ,
6 3
p p "
29 ,6 3
p p l "
29.
6
pl .. l< 12
\ l
12 1378
2
= = .
2. Ans. 010D .
( ) ( )
( )
( )
4 24
2 2 22 2 2
2 2 1 2
1 1 . 1
+ - ++= - =
+ + +
, = = 1
\G 0
10 1
+ -=
2 0
10 1
- = +
= 10 + 0 = 10.
3. Ans. 035
(0,0). I
, , . , . , (0,0) (3,4) . =
7C
3= 35
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4. Ans. 009
( ) ( )
( )
1
1 1
+ +=
+ +&
( ) ( )( ) ( )
1 2 , 0,
,0 ,2
1 2 , ,0, ,2
2
- p p p
= -p p p + = - p -p p p
() = 2p,p,p,2p () = 0 = 0\ = 4, = 5 + = 9
SECTION-IV
1. Ans. 7
Q ( ) ( )( ) ( )4 4
4
0II I0 0
A . .= = - 4
2
0
40 . 9 = - + L 9 + 2= 2 = 5
2
3
40 = -
( )3 31 98 22
40 5 3 403 3 3
= - - = - =
\A = 72. Ans. 4
Q3 24 4 . 10
3 = p = p =
2 10
4 =
p...(1)
A, = 4p2
58 . 5 8 .
8 = p = p =
p...(2)
(1) (2)
2
10 5 4
4 8 = =
p p3. Ans. 6
( ) ( ) 1 1
1 1 1 1
5 1 5 4 3 5 4 5 1
= =
= - - - - -
1 1
5 5 5 2
1 0 0
1
3
- -
=
= -
1 1
5 5 5 2
1 10 0
1
3
- -
= =
= -
( ) ( )1 1
5 10 3 8 13
0 0
11 .... 10 ....
3
= + + + + - + + +
1 1 13 3
5 5 5
0 0 0
1 1 1 1
3 1 1 3 1
-= - = - - -
1 2 2
4 3 2 4 3 2
0 0
1 1 1 1
3 1 6 1
+ + + += =
+ + + + + + + +
Q1 2 2
4 3 2 4 3 3
0 1
1 1
1 1
+ + + +=
+ + + + + + + +
1
=
\ = 64. Ans. 8
C 1=2,
2= 3 (00,01,10)
.
I
0 (1)
1
.
1 0
\1 0 (2)
2.
=
1+
2...(1)
1
2
1
-
-
- = A,
2
5 6 5 6 55 5
4 4
- -= =
,
5=
4+
3= 2
3+
2= 2(
2+
1) +
2
= 32+ 2
1= 3 3 + 2 2 = 13
\G = 13 5 1 = 8
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1. Ans. (2)
11.8
6 83 2
6 8
+ +
+
8I I
6 8
= + 2. Ans. (1)
/.
3. Ans. (3)
4
( )
4
5 4
427 27310
10
+= = 7000 K
4. Ans. (4)
80 90 40- q - q q -+ =
l l l
5. Ans. (1)
L= 24 10 W
=
12 102
= W
6. Ans. (3)
(100 + 10)(q 10) = 330
(90 q)
4q= 280 q= 70C7. Ans. (4)
BF
= DE
BF DE2
Dq Dq = D D l l
HBF
=DE
1H
2
BF
= 2DE
.
8. Ans. (4)
0
2
1
2
=0
GM
SOLUTION
Path to Success
ALLENCAREER INSTITUTEKOTA (RAJASTHAN)
TM
CLASSROOM CONTACT PROGRAMME(ACADEMIC SESSION 2014-2015)
TEST # 02 (Pattern : JEE-Main)
Date : 29 - 06 - 2014TARGET : JEE (Main + Advanced) 2015
ENTHUSIAST COURSE (Phase-I)
PAPER CODE 0 1 C T 2 1 4 0 1 6
9. Ans. (3)
= I
45 = 3( + 1 + 8)
= 6W10. Ans. (2)
(e I).
11. Ans. (3)
I=
20
11000
20I
100010000
1000
=+
+
II I
1000 2
= = +
12. Ans. (1)
( )KA 30H
q -=
l
( )480 4 10 302
0.8
- q -=
13. Ans. (2)
( )10
I 2A C1 1 3
= =+ +
1I 2 =
= 4
14. Ans. (3)
F
As =
F
= 3 F
F
= F
(2 )
= 0.5 15. Ans. (1, 3)
B D .
I A B .
16. Ans. (3)
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17. Ans. (1)
C
4W& 6W
=( )
230
3
= 300
I =30
10A3
=
18. Ans. (4)
19. Ans. (4)
Dl= laDq0.06 = 60(12 106) (q 0)
q=1000
12= 83.33 C
20. Ans. (1)
1
1 2
31
h = = +
()
( )
2
1
1
/10
h =+
, 21
6h =
21. Ans. (4)I = 2
e=
+
=B .
C22. Ans. (3)
23. Ans. (2)
24. Ans. (2)
I F =1 2
2
G
F =( ) ( )
( )1 2
2
G 2 / 2 F
93=
25. Ans. (3)
26. Ans. (3)
.D. = 2
1= E ( q
1 q
2)
27. Ans. (1)
=C
Q
= 800 10 106
= 66
1050
1010800
A.
28. Ans. (4)
.D. = (2
1)
2= 0
1=
0
1
4
-
p 29. Ans. (1)2
2
0
1 1
4 2
= p
9 10912
36 10
2
-
= ( ) 21
0.1 2
30. Ans. (3)
= 201
E 2
= ( ) ( )2 2
0
13
2
=
0
=
= = 50
3
2
31. Ans. (1)
32. Ans. (3)
33. Ans. (3)
34. Ans. (3)
35. Ans. (4)
36. Ans. (3)
37. Ans. (1)
38. Ans. (1)39. Ans. (2)
40. Ans. (4)
41. Ans. (2)
42. Ans. (3)
43. Ans. (2)
44. Ans. (3)
45. Ans. (2)
46. Ans. (1, 2)
47. Ans. (3)
48. Ans. (2)49. Ans. (1)
50. Ans. (1)
51. Ans. (3)
52. Ans. (4)
53. Ans. (1)
54. Ans. (2)
55. Ans. (4)
56. Ans. (3)
57. Ans. (1)
58. Ans. (1)
59. Ans. (2)
60. Ans. (2)
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61. Ans. (4)
( )
3
22 3 0
3 3
1 3 .
- - -
( ) 2 22 2 03 1 3
1 3 1 3 = - ---
( )
2 2 4
2 2 2 0
3 3 1
1 3 .
- + = - -
( ) ( )
( )2 2 2 03
9 11 3 . .
- += + -
-
13 2 8 6
3
= - + =
62. Ans. (3)
( )3
0
I 6 = - = 62q/ 4
2 2
0
6 .6
p
= q q 12 qqq/ 4 / 2
2 2
0 0
918 2 9
4
p p p= q q = q q =
63. Ans. (3)
() = 3( 2)2/3 ( 2)
( )( )
1
3
2 1 0
2
= - =-
( 2) = 8 = 10\
( ) 1/3 2 / 3 0 2 10 20
3.4 2 0 4 3.18 18+ -
0
64. Ans. (2)
( )( )1 1 2 3
0 0
1 1 1 ....
2 3
+ = - + -
l
2 2 2
1 1 11 ....
2 3 4= - + - +
, 2 2 2 2 2 21 1 1 1 1 1
1 ... 1 ...2 3 4 2 3 4
- + - + = + + + +
2 2 2
1 1 12 ...
2 4 6
- + + + 2 2 2 2
22 3.
6 2 6 12 36p p p= - = =
\ = 36
65. Ans. (1)
() ( - a) () ( a) ( 1) ( & > 1)
66. Ans. (2)
( )2
3 3
1 2 2 A
-= - =
\ ( )2
3
2
-=
& ( ) ( )3 2 2
6
.2 2 .3
- -=
( )2 2 24 4
2 3 2 6
- - -
= =
( ) ( )4
6 6
+ -= -
\L 6=
& ( )
4 6
96 6= = \( + )
= 15
67. Ans. (4)
( )( )
1/
1
0
0 0
1 3 1 3
1
++
=
1.3
3
0
= =
68. Ans. (2)
( ) ( )
( )
( ) ( )( )
2
0
() ()
.
. . () . ()
=-
( )( ) ( ) ( )
2
. =
-
( )
( )
( )
( )
2
1 1
2014
= =
-
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69. Ans. (1)
P(1,4)Q(4,5)
R(m,m)
= . L
(5,4) , = 4,
& = .
\ = 470. Ans. (4)
62 + 42 (3 + 4) (2 3)\4 = 12
= 371. Ans. (3)
2= I
3= 2= I + = 2 I
4= 22 = 2(I ) = 2I 3
5= 2 32= 2 3(I )
= 5 3I
6= 52 3 = 5(I ) 3 = 5I 8
\ = 672. Ans. (3)
1 1
1 2
1 2
+ -D = + +
- +
2
2
1&
3
3
1
1 1
1 1 3
1 1 1
+ -
= -
-
= (4) ( + 1) (4) + ( 1) 0 = 04( 1) = 01
2
= -
73. Ans. (4)/ 2 / 22
2
/ 2 0
I
1 5 4
p p
-p
p= = =
+ 74. Ans. (4)
L-H :
12 8
5 8 2
1 5 8 2 1 26 2 7 6 2 6
+ + = =+ +
75. Ans. (1)
( ) ( )( )5
4
1I 3 3
3= + =
( ) ( )( )15
12
17
12
+
76. Ans. (3)2 4 8 16
= p = p =
2
=
p
,34
3= p
2 2 24 4 8
= p = p =
p77. Ans. (3)2
1
I
=
l; l = =
2
2
1
I
= =
78. Ans. (1)
L () = A4+ B3+ 2
A ( )2 0 1 =
, ()= 4A3+ 3B2+ 2
= (4A2+ 3B + 2)
Q = 1 & = 2 () = 0
\2
2 4A 14A
= =
&3B
3 B 14A
-= = -
\() = 4 3 21 4 - +
\(2) = 48 + 4 = 079. Ans. (1)
C3C
3 C
1
1 1 0
1 1 0 0
1 1
+ q =
q (3),
q(1 + q 1) = 0
q = 0 3
,2 2
p pq =
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80. Ans. (4)
3 3
q=
- q
\ 3 3
q=
q\
( q) ( )3 3 3 3
q= - q
q
\ 3 3
1 27
- = -q q
\3 3
126 26
- =q q
\A D 1 26 262 3 3 q= q
1692
3 3= q
\M 4
pq =
81. Ans. (4)
() = 12 9+ 4 + 1;
(x) i s (+)ve for x < 0
> 1 () = 9(3 1) + (31) +1
() > 0A 0 < < 1 () = 12+ 4(1 5) +1
\() > 0.82. Ans. (2)
L C (,)
\
11
4 0 1 182
0 12 1
=
12 4 + 48 = 36
3 + 12 = m 9(3 + 12)2= 81
83. Ans. (3)
F 1 ,2 2. 4
0 4
+ = = -
2 ,2
2
163 16
3= =
Q
2 3
4 16 641 1
3 3
- = - =
64 4
1 3.16 3
= =
84. Ans. (1)
1
0
1
0
1 2 ... 1
1 2 ... 1
aa a a
b-ab b b
b
+ + + b += = + + + a +
85. Ans. (2)
( )2 1
- +=
Q > 0 2 + 1 > 0 " +
D < 0
1 4 < 0
1
4
.
II A.M & G.M
86. Ans. (3)
L
L &
L
= 83
2
=
\ 2
18 3
+ =
\1 3 3
.8 2 16= - = -87. Ans. (3)
( )2
1
+ =
( )2
-=
88. Ans. (1)
.
0 3 3
= =
= l389. Ans. (3)
(a) = a& 90. Ans. (3)
22 4 1 24. 4
2 4 2=
( )81
2 8
-= +
\1
A16
= -
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PART-1 : PHYSICS SOLUTION
PAPER-1
Path to Success
ALLENCAREER INSTITUTEKOTA (RAJASTHAN)
TM
CLASSROOM CONTACT PROGRAMME(ACADEMIC SESSION 2014-2015)
Date : 20 - 07 - 2014TARGET : JEE (Main + Advanced) 2015
ENTHUSIAST COURSE (Phase-I)
HS-1/7
PAPER CODE 0 1 C T 2 1 4 0 2 2
SECTION-I
1. Ans. (B,C)
2. Ans. (A,C,D)
3. Ans. (A,B)
Sol. L : . ,
: ,
4. Ans. (A, B,C)
Sol. H 2
ratedV
RP
=
2
V
R
5. Ans. (A,B,D)
Sol. A = 0, & = 0.
A = , =2 A;
C= 0.
6. Ans. (A,C,D)
Sol. =( )1 1 2 2 1
1 2
a - a D
+
l
7. Ans. (B,C)
Sol.
2T05R/6 R
Tx T0
( )0 6 2 5
-=
( )0 06 2
11
-=
8. Ans. (A)
Sol. 200 = 1 200 =
2 100
1= 400 J,
2= 300 J
9. Ans. (D)
Sol. 2 K
K E 22
1E 77 K2
1
= =
10. Ans. (B,C)
TEST # 04 (Pattern : JEE-Advanced)
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SECTION-IV
1. Ans. 5
Sol. I 0 0
050
4.45.5
- +
0= 40
\ 0= 0\ 1.1 2
050
1.15.5
- +
0= 2
10 = 2
\ = 52. Ans. 9
Sol.0
1 1 1
4
= + - p
3. Ans. 4
4. Ans. 8
Sol. J :
I2 > (
).
B , 10 A. ,
( )21 1 1I p l ( ) l ,
, I
1
1
.
2=
1/16. , I
2
2
2 2 2I p l ( )F,
I28I
1= 8.0 A.
5. Ans. 2
Sol. 20
E
4 =
p
0
E 2
4
= - - p
,
11 1
0
E 2
4
= - - p
22 1
0
E 2
4
= - - p
,
1
2
2 1
E E
- =
1
2
0.3 = 1
2
2 =
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6. Ans. 2
Sol. D .q v
rv0
dQ
, 1 & .
0 =
&2 2
0
1 K 10
2 2+ = +
2
2 00
1 K 1
2 2
= +
22
0 2
1 K 1
2
- =
( )2 2 201
K2
- =
( )2 2 2 20 01 1
K 02 2
- - =
( )2 2 4 2
0
2
0
K K
+ += = 2
K = 9
2
0 12= = 1
7. Ans. 3
Sol. C & D , .
( ) ( )1
2I
2
e e= =
+ +
C & D = ( )1I
2
-
(0) =
( )( )
e -
+
140 = 420
- +
1 2
3
- = = +
, C D ,
2I 22 2
3
e e
= = +
3 3 420 3154 4 e = = =
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C C & D
0 2 2
I I I
= -
+ +
= I2
-
+
315 121
3
=
= 5W, = 10 WF,
D
C
BA
r=5W
420V
R=10Wr=5W
R=10W
5W
, KL & KCL, C & D = 12 A
8. Ans.2
Sol. L & , .
= ( )rx
R xr x
+ -+
,
( ) ( )
0 0A
I r V r I
r x rx R x r x
= =
+ + - + ,
AdI 0dx
=
=R
2
, ( ) ( ) ( )
( )0
A min
12 2V rI
R 4 2 1R r
4
= =+ +
= 2A
9. Ans. 2
Sol. F 1 2
r R R=
= ( ) ( )xR 1 x R - = ( )R 1 x-
( )
R 1
r x 1 x-
-
R
r
1x
2=
R
2r =10. Ans. 8
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PART2 : CHEMISTRY SOLUTION
SECTION-I
1. Ans. (A, C)
2. Ans.(A,C)
3. Ans.(B, C)
4. Ans. (B, C)
5. Ans. (C, D)
6. Ans. (C, D)
7. Ans. (B, C, D)
8. Ans. (C, D)
9. Ans. (B,C)
10. Ans. (C, D)
SECTION-IV
1. Ans. 6
2. Ans. 6
3. Ans. 1
1 2 A B C
, 1>>
2
\A 2k C
C = A
0 2
k t[1 e ]--
210 1010[1 e ]
-- = - 0.110[1 e ]-= -
10[1 0.9] 1= - =
4. Ans. 4
5. Ans. 2
6. Ans. 2
7. Ans. 4
8. Ans. 5
9. Ans. 6
10. Ans. 6
PART-3 : MATHEMATICS SOLUTION
SECTION-I
1. Ans. (B,D)
6 2 5 > 0 (1,5)
( ) ( )
2 3 2
0
3 2 2 2= + + = + +() (1,5)
\ = 4, M = 1602. Ans. (D)
. 2
q = =
rr
rr
4 4
22 2
4 4
+ +p p
p-q
= =p p
- -
4 4
22 2
4 4
- -p p
p-q
= = -p p - -
\L .
3. Ans. (B,C)
(+1
) + 2
( + 1)
+1= 0
+1
= 2(+1)
\( )
1 1
1
1
2 4
-- +
=
p= + =
4. Ans. (A,C,D)
( )( )2
1
=
+Q () 1,) () > 0 () () > 1
( )( )
( ) 12 21 1
1
-= ++ +
Q(1) = 1 ( ) 14
p +
5. Ans. (A,C)
1 3 1 2
1 4 2 3 0 0
2 3 1 3 3
- +
- - + = =
+ -
& = 3
6. Ans. (A,C,D)
B I7. Ans. (A,C,D)
R
EP Q
H O2
1
C &
2 : 1 5 8
,3 3
, E
E & E(2,5) G E 2 : 1 (9,2)
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\E ( 1)
2+ ( 2)
2= 80
8. Ans. (B,C)
() 0,1
() 0,1, (0,1) & (0) = (1)
\b 1 1
,3 4
- -
9. Ans. (A,C)
L L
2 0 55 33 5 33
1 1 0 ,4 4
1 2
+ -- m = m =
m10. Ans. (C)
( ) ( )
2 2 2 21
I
1=
+ + l
...(1)
21 1
,
= = -
( ) ( ) ( ) ( )
1
2 2 2 2 2 2 2 21
I
1 1 = = -
+ + + + l l
(1) & (2) 2I = 0SECTION IV
1. Ans. 9
L () = 4+ + 5
() = 43+ = 0 1/3
4
- =
1/ 3 4
3
256 0
4 27
- >
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5. Ans. 7
1 2 0 1, 2+ + - = = - =
11
22
03 2 3 2AB
0 4 4
+ + = =
- + - +
\ 113
, 8 282
= = =
22= 7
6. Ans. 5
QP
xy=1P(sinA,cosB)Q(tanC,cotC)
(A, B) 2+ 2= 1
(C, C) = 1
\
(C A)2+ (C B)2= ()2
( )2 2
C C 1= + -
( )
2
2 1 3 2 2= - = -7. Ans. 2
1 1
1 0
0 11
2 1 0
++
+
- - =
r r r
11
1 0 0
0 11
2 1 0
- - =
r r r
22
2 1 0
0 11
2 1 0
- - =
r r r
1 0
0 11
2 1 0-
- - =
r r r
\ 0 0 a b
= + g d
r r r
4 2
15 5
2 4 05 5
- =
4
5
25
=
1 1 1 1
....4 16 64 5
a = - + - + = -
1 1 1 2....
2 8 64 5b = - + - + = -
1 1 1 2....2 8 64 5
g = - + - =
1
5d = a = -
8. Ans. 0
( )( )/ 4
3
0
2 1
1 I
2
p + +
+=
l
( )2
/4
1
0
2 1
1 2
p
-
+ ++=
l
( )2 1
4
2
0
1 1
2
p + +
=
l
l
1
4
p = +
l
9. Ans. 7
2 - +rr r
= 2 2 2 4 4. 2. 4.+ + - + -r rr r r r
13 6 2= -
\ + = 710. Ans. 4
L + 4 = =
2 2y 4 4 y
2
y 2 y 4y 4I e dy e e dy
y y
- - - - += =
y 4 4e 1 Cy
- = - +
xx e Cx 4
= ++
a= 0 & b= 4
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PART-1 : PHYSICS SOLUTION
PAPER-2
SECTION-I
1. Ans. (D)
Sol. 2B q= 20I
2
m p
2. Ans. (B)
3. Ans. (B)
Sol. C ( )
E
= G
E
= G
E
= G
E
= G
E= E
E
= 0
E
= E
E
= E
+ E
= 2GM
R
Eext
Ein
Eself
Eext
E
= 2GM
2R
A E
E
.
E
= E
= 2GM
2R4. Ans. (C)
Sol. 60 3 2GM
100 5 R= =
A ( )
2GM 1 GMR 2 R
- + = -+
2 2GM 2GMR R
= -+
9 2GM 1 1
. 2GM25 R R R
= - + ( )
9
25R R R =
+
=9R
16
5. Ans. (B)
Sol. R R
R 2 R4 2
= + =
CLASSROOM CONTACT PROGRAMME(ACADEMIC SESSION 2014-2015)
TEST # 04 (Pattern : JEE-Advanced)
Date : 20 - 07 - 2014TARGET : JEE (Main + Advanced) 2015
ENTHUSIAST COURSE (Phase-I)
PAPER CODE 0 1 C T 2 1 4 0 2 3
Path to Success
ALLENCAREER INSTITUTEKOTA (RAJASTHAN)
TM
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Kota/01CT214023
6. Ans. (B)
Sol. min6t2
3
4
t
)20(k
t
2
)30(k4
2
==
=
=
7. Ans. (B)
8. Ans. (B)
Sol.0
1
IB
2R
m=
( )
2
02 3 /2
22
IRB
2 R 2 2R
m=
+
9. Ans. (C)Sol. F B & A
10. Ans. (C)
Sol.E
F
=r r
11. Ans. (C)
Sol. O .
12. Ans. (B)
13. Ans. (B)
14. Ans. (D)15. Ans. (B)
16. Ans. (D)
Sol. (15 and 16)
Q KS
= -
4 4
= - -
A B
K4, 12
= - = -
A B
Q Q Q
= -
= KS 4 + 12 = 100 0.1 8 = 80
17. Ans. (A)
Sol. 2G
=
< :
= :
> :
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18. Ans. (D)
Sol. (Moderate) = C= 1 2 mC = 2 mC = C= 1 4 mC = 4 mC\N 4
= 4 2 = 2 mC 4
= ( ) 4 = 8 mJ
D =2 2
1C( )
2- =
1
2 42 22 mJ = 6 mJ
N
DH = D = 8 6 = 2 mJ
19. Ans. (A)
Sol. ( )0 RI
B 5 R
m= qp
( )0 1 2I
B 4
m= q + q
p20. Ans. (C)
Sol.
= -
= -g
PART2 : CHEMISTRY SOLUTION
SECTION-I
1. Ans. (D)
104=
2x
1 x-, = 102, H = 2
104=
4 2
4
(10 )
C 10
-
--
C = 2 10
4
2 104= 1
= 5000
A = 4999
2. Ans. (B)
C5H
5NH++ H
2O C
5H
5N + H
3O+
0.01 0.002 +
103 =x(0.002 x)
0.01 x
+-
= 2 10
3
H+ = 0.002 +
= 4 103
3. Ans.(B)
4. Ans. (C)
5. Ans. (B)
6. Ans. (A)
7. Ans. (B)
8. Ans. (B)
9. Ans. (A)
10. Ans. (D)
11. Ans. (B)
12. Ans. (D)
13. Ans. (C)
14. Ans. (C)
15. Ans. (C)
16. Ans. (A)
17. Ans. (A)
18. Ans. (A)
19. Ans. (C)
20. Ans. (A)
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Target : JEE (Main + Advanced) 2015/20-07-2014/Paper-2
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PART-3 : MATHEMATICS SOLUTION
SECTION-I
1. Ans. (B)
r
( ) . =r r
( ) 3 4 3 4 4 6 .
5 5
+ += +
( )18 3 4 25
= +
2. Ans. (D)
1 1 1 1
1 . . . .
- -
+
1
1
= +
1 1
0
1 1
1
+= + = =
+
3. Ans. (A)
( )
( )
( )
2 40
.10 .2 40 40
= = +
l
( )
2 .10 .2
40
= +l
4. Ans. (B)
C ()
- ()
3, + 3
+ = 2 =
2-
\ + =
-
N, . 2( + ) + .(+)
= .2
.
- + -
= .0 + .0 = 0
(Q
= - () = 0).
5. Ans. (D)
QM. 1 + 2 1
1,2
. + 3 3
0,3\M. 1 + + 2 + 3 4 1,2 0,3.
\1 2
1 50 3
+
6. Ans. (B)
Q . 014243
,6 2
p p
7. Ans. (C)
P = q, = q (q) = 8(q+ q).(3q+3q)= 8(q+ q)2(1 qq)\(q) = 8(1 + 2qq).(1 qq)= 4(1 + 2q)(2 2q)
2q
= \
1,1() = 4(1+ ) (2 )
\()
=9
4.4
1
2
=
\ = 9.8. Ans. (A)
Q 1 1,1,1 1,0,0
\N
= (3 33) 2 = 1629. Ans. (A)
Q( )
( )
0
1
=
+ P =
\
( )( )
1
0
1
=
+
...(1)
0
+
\(1) ( )
( )
1
00
1
+=
+
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( )( )
1
00
0 . 1
+=
+ ...(2)
( () 0,)
( )
0
+
L.H.S (2) 0
A,( )
0
0
+
L.H.S (2)
,( )
0
+= (0,)
(0) = 0N (2)
( ) ( ) ( )( )( )
11
00
0 1 0 1
0= = + =
+ l
( ) ( )1/ 01
0 1
=-
10. Ans. (B)
() = 2
+ ( 1) 1/4+
4 +
4 > 0 " R " R.
2 ( 1) +1
4
< 4 +
4 "R " R...(1)
Q 4 +
4
1
2
\(1) ( )
2 1 1
1 R4 2- - - + "
2+ ( 1) +1
4> 0 " R
D < 0 ( 1)2 4.1
04
( 1)2< 1 0,2
Paragraph for Question 11 and 12
11. Ans. (B)
QAC A(2,6) S2
\ AC 4 36 4 24 11 9 3= + + - - = =
\AB = 2 3 = 6.
C
B
A
(2,6)D
S2
E
P
S1
12. Ans. (C)
M AP = AE
= AD + DE
= 5 + 4 = 9.
Paragraph for Question 13 and 14
13. Ans. (C)
+ + = 4 ...(1), 2 + + 3 = 6 ...(2) + 2 + = ...(3)
S (1) (2) = 2 2 = 2+ (3), = 6
H, , 0, R\N. = 20 21 = 420.
14. Ans. (A)
F = 0, 6N. = 1 20 = 20.F , = 0 = 6 N.
= 1 1 = 1.
\ = 20 + 1 = 21.
Paragraph for Question 15 and 16
15. Ans. (C)
E ( ) 0 - = = +r r rr r r r
( ) 2 3 2 = + - + - +r
L M ^ P(0,1,2)
\ ( ) ( ) ( ) PM 2 1 1 5 = + + - + -
Q ( ) PM. 2 0- + =2(2 + 1) 1.(1 ) + 1.( 5) = 0
4 + 2 1 + + 5 = 0
2i j + k
M(2t+1, 2t, t3)
6 = 4 2
3
=
\7 4 7
M , ,3 3 3
= -
\S = PM
49 1 169 219
9 9 9 3= + + =
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16. Ans. (B)
L R xi yj= +r
C
2+
2 2 + 2 + 1 = 0 = (1,1)
N L
(1,1,0). M. 2 3= .
17. Ans. (B)
(P) G....
= =
,....
. 1
=l .. l = 1
1 1
1
= = =l \ = 1
(Q) [ ] [ ]( ) [ ]( )6 2 6
2 2 2
- -
= +
[ ]( ) [ ]( )6 2
2 6
3 0 3- = + =
(R) Q ( )2 2 22
5 3 2+ + - = + = - =r r rr r r r r
(S) A
( ) ( ) 3 3 9 = + + = - r r r rr r r r
8 8 30 4= = =r rr r
18. Ans. (C)
(P) P - ,32
p=
(Q)2 3 3 0 1
= - = =
N (0) = 2, (1) = 0, (2) = 106=4
\ 4.
(R) ( )( )
2
2
2 0
2 0
- >=- +
= + 0 (0,1)\ = 0
(S) Q ( )
0
1
0
1
+= < -
() = 0
\ ( ) ( )
( )
2
2
0
1
1 0
1
> +=
< -
A, (0+) = (0
) = 1 (0) = 1
\ ( )( )
2
1
1 =
+
(1 + )2.() = 1
19. Ans. (C)
(P) E S1 S
2= 0
+ 5 = 0
0
5q
M P
x+y+5=0
N0 0 5 5
OM2 2
+ += =
5 / 2 1
455 2
q = = q =
22
pq = \ = 2
(Q) (C1C
2)
2 =
2 +
2
(5 2)2+ (6 3)2= 22 = 3
P
r r
C2C1(2,3) (5,6)
90
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(R)
1 2
2 3 0
3 2 1
- -
- =
-
2
3 4 = 0 ( 4) ( + 1) = 0 = 1,4\
1+
2 2 = 1
(S) QA2= O A= O > 2 N
\ (I + A)6= I + 6A = 620. Ans. (D)
(P)
2
6 2
1 .2
1 =
+
( )
( )
5
26
1 6 .2 2.6
1
+ -
= +
2
2
1
4 122
4=
-= = -
(Q)
1
2
1
(x | x x |)dx-
- - = ( )1
2
1
-
- -(Q )
( ) ( )
0 1
2 2
1 0
5 1 1
6 6-
= - - + - = - - = -
(R) L1
= ,
[ ]2
1 2 3 ....
+ + + +=
[ ] [ ]( )2
1 1
2 2
+= =
(S) Q = 6 2
...(1)
1 2
= - 3
1
= + ...(2)
2
31
= -
= 1A = 1, = 4
(1) (2)
(1,4)
1
3
=
= -
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PART-1 : PHYSICS SOLUTION
PAPER-1
Path to Success
ALLENCAREER INSTITUTEKOTA (RAJASTHAN)
TM
CLASSROOM CONTACT PROGRAMME(ACADEMIC SESSION 2014-2015)
Date : 27 - 07 - 2014TARGET : JEE (Main + Advanced) 2015
ENTHUSIAST COURSE
HS-1/8
PAPER CODE 0 0 C T 2 1 4 0 0 1
SECTIONI
1. Ans. (B,C,D)
2. Ans. (A,B)
3. Ans. (C,D)
4. Ans. (A,B,C)
5. Ans. (A,B,C,D)6. Ans. (A, B, C)
Sol. = w + wr
= = w + w + -w w + w wr
r
1 =
2
2 2
1
w=
+ w
r
7. Ans. (A,D)
Sol. O , .
\T
k C12
k C22
V
8. Ans. (A, C)
Sol. E.F. =0
3
re
r
P = R1 R
2
= ( ) ( )2 2 2 21 20 03R 3R 06 6r r- - -e e9. Ans. (A, B, C, D)
Sol. V = E.
V =
2
C 1 1 C
- = - E = 2 2C V 1
1 1
= -
F = E
0
= E
= 2 E.F. = .
COMMON TEST # 01 (Pattern : JEE-Advanced)
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10. Ans. (A,B,C)
Sol.
2
00
F F
R
=
r , &
F. 0=
r r
W =
2R 2
200
F .
R
r
=
2R3
0 020 0
8F RF
3 3R
=
SECTIONIV
1. Ans. 5
Sol. A (Q0 ) &
\
( )0K Q K
R
--
=
[ ]0
......()
Q 2
R
=-
()
Q =
2
0 RQ 1 2
- -
2. Ans. 6
Sol. F ,
( )2 22 2A A A 1.52 2
A A
r -r r+
= =r r
ll
l G
5
3
6
2 4
7
8
l
( r , A 2, 3, 4)
3. Ans. 9
Sol.A
BCD
I
O (B + C)
N B = 12 6 C
& C = 6 3C
N (B + C) = 54 C
T = 54C
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4. Ans. 4
Sol.
48 V
a
b8W
5W
4W
= 12& V
= 17 12 = 204 V
5. Ans. 1
Sol. R = N
=N
= l2p NR
N
2 R
l=
p= = s
F =
( )3/2
2 20
E NPRP
2 R
l =
+
F =( )
03/2
0
160 0.1 1
2 1 3
+= 1
6. Ans. 2Sol. W s s.
W =2 2
0 0
R R2 2
s s + - -
W =0
.2
s
= 2 2
0
R R2
s + -
7. Ans. 1
Sol. a=2
R
aamg
34
R
R
Rhs
j
A -
R(1 a) + =21
2,
2= 2R(1 a) + P N , :
a=( )2R 1 2
R
- a + =
3 1 R
2
a -
\ =
1R
8
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PART2 : CHEMISTRY SOLUTION
8. Ans. 5
Sol. 0 B = m r
l
B 2p = 0
2
0
J 2
p 9. Ans. 9
Sol. () L= L
; w
12
m 2l= MV
2
l V =
M6
m lw
m
V1
w
0 VM
() P= P
; 0 = MV V
1 V =
M
mV1 1V
6=
wl
() =1=
02
)V(V 1
-w--
l V + V
1=
2lw ;
6M6m ll w+w =
2lw ;
+1
Mm = 3
Mm = 2 M =
2m = 9 .
10. Ans. 5
Sol. 3 q 3 q= 3 ... ()
3 q R =23R
2a ...... (I =
23R
2) ... ()
= aR ... ()
= 0.5
SECTION-I
1. Ans. (A,B,C)
2. Ans. (B, C)
3. Ans. (A , C)
4. Ans. (C)
5. Ans. (A, C, D)
6. Ans. (B , C, D)
7. Ans. (A , C , D)
8. Ans. (D)
9. Ans. (A , B, D & B, C, D)
10. Ans. (D)
SECTION-IV
1. Ans (12) [OMR Ans. 3]
2. Ans (75) [OMR Ans. 3]
3. Ans. (13.30) [OMR Ans. 4]
4. Ans. 4
5. Ans. 2
6. Ans. 7
7. Ans. 2
8. Ans. 3
9. Ans. 2
10. Ans. 6
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PART-3 : MATHEMATICS SOLUTION
SECTION-I
1. Ans. (A,B,C,D)
1 33 0
7
- - p >
1 3
3 7
-p < < p
7 7
3 6
- < < 2.33 < < 1.16
= 3,2,1,0,1
2. Ans. (B,D)
( )1/
3
3 0
2
-
-=
( )3 0
1
2
-= ...(1)
( )3
0
2 3
- = -
l
...(2)
(1)
4 3 3
3 0
A B C D E 1
2
- + - +=
A C,D,E = 0
0
A B 12 2
- = B 12
- = B = 2
() = A4 2
3...(3)
(2)
( )3
0
2 3
- = -
l
0
A 1
A2 3
A 2
2
+ = -
l
A
1. 32 = - A = 6
() = 64 2
3
() = 243 6
2
(1) = 30 A 3B = 0
3. Ans. (A,B,C)
3512
1 = (8 + 1)256
1
= (1 +256
C18 +
256C
28
2.......+
256C
2568
256) 1
=256
C181+.........
3512 1 = 211 INTEGRAL
3512
1 23,2
7,2
11
4. Ans. (A,B,D)
1 2 117 6 2 2
- - p - + + =
...(1)
2 171 6 1
2
- - + =
( )2 1
1 3 12
- - - =
L 1 1
2
= - ,
.
2
17 D 1 6
2 4 2
= - + = - = -
= 1
(1) 1
,12
-
5. Ans. (D)
2= 3
2 + 2
2 =
5 2
2+ ...(1)
2 = 2 " + ()2= 2
23 2 2
2
2 " 2
4
+ = -
4+
3" =
4
22
2 2
4
22 2 1
2 4
= - -
25 1
2 4
= -
= 6
6. Ans. (B,C)
( )3
1
0 0 1
2 1 2- + +
= p + <
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() (1+) = (1
)
( )22 1 1
12 3
1 ==
- p p + = +
1 10 3
2 6 + = =
(1)13
2 4 4 6
p p= - - = -
7. Ans. (A,B,C,D)
2() +
2() = 2( 1) =
2( + ) ...(1)
", R
= = 0 (0) = 2
(1)
( ) ( )( ) ( )( )
0. 0 2
-+ +
( ) ( )( ) ( )( )
+ -= + +
I 0(0) ((0) + (0)) + 2 = ().2()
2 (0) () ()+ = =
( )22 2 (0)
2 2+ + = ...(2)
= 0 = 1
2= (0) = 0 ...(3)
(2) ( ) 2 2 = +
( ) 3 11 3 = = , ( ) 7 3=8. Ans. (A,B,D)
= 51 + 57 = 254 3
= 50 + 58 = 254 4
= 49 + 59 = 254 5
3 4 5= =
3 > 4 > 5
> > , > & >
+ = 254 (3 + 5)
= 254 (24 1) > 254 4
+ =
9. Ans. (C,D)
( )
2
1
2
1
2
1 2
-
- =
+
(2 + 1)p
() = 1
() 0,p) 1() = () ()
() = 1
() = 2p "(p,2p)() = 1 " (p,2p)
10. Ans. (A,C)
( )
= +
l l
[ ] [ ] 1 1 = - + -l l = l + l
0 I()
1 I
=
-
l
l
R = 1,0
() = 0 l = = ( I), = 0 = 1() = 1 l
SECTION IV
1. Ans. 9
() + () = 2& + = 2
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