IIT-09-STS6-Paper2 Qns.pdf Jsessionid=DNIPNGLEGLCG (15).PDF Jsessionid=DNIPNGLEGLCG

8/13/2019 IIT-09-STS6-Paper2 Qns.pdf Jsessionid=DNIPNGLEGLCG (15).PDF Jsessionid=DNIPNGLEGLCG

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PART A : MATHEMATICS

SECTION I

Straight Objective Type

Th is s ect ion con t a in s 9 m ult iple ch oice q u es tion s n um ber ed 1 t o 9. E a ch q u es tion h a s

4 choices (A), (B ), (C) a nd (D ), out of w hich ON LY ONE is corr ect.

1. The int egra l va lues of x for w hich x2+ 5x + 8 is a perfect squa re are

(A)4 and 5 (B)4 and 1 (C)1 and 4 (D)4 and 5

2. The proba bilit y t ha t t he lengt h of a ra ndomly chosen chord of a circle lies

between1

2a nd

4

5of its dia meter is

(A)2

5(B)

5

6(C)

36

100(D)

39

100

3. I f , 2be the imagina ry cube roots of unity , then

(100 + 100+ 1022)6(50 + 55+ 50

2)3is equa l to

(A)61 (B)0 (C)61 (D)16

4. The va lue of k if the eq ua tions x2

+ 3x + 4k = 0 a nd 2x2

+ 5x + 7k = 0 ha ve a

comm on root is

(A)1 (B)1 (C)2 (D)2

5. In a n A.P. of 93 term s, th e 47th t erm is 25. Then t he sum of series is

(A)6225 (B)5065 (C)9325 (D)2325

6. I n a n exa m in a t ion t her e a r e 10 m ult iple ch oice q uest ion s a n d ea ch q uest ion h a s4 choices. Number of w a ys in w hich a stud ent can fa il to get a ll answ ers correct is

(A)1142 (B)4

101 (C)10

41 (D)10

44

Brilliant Tutorials Pvt. Ltd. IIT/STS VI/MPC/P(II)-2

SPACE FOR ROUGH WORK


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7. I f P a nd Q a re sq ua re ma trices of sa me order such tha t (P + Q)2

= P2

+ Q2

+ 2P Q,

then

(A)P = Q (B)P = Q (C)P Q = QP (D)P = Q

8. If A, B, C be three equally and collectively exhaustive events and the odds are 5 : 2a gainst A, 7 : 3 a gainst B , then the odds aga inst C is

(A)41 : 29 (B)53 : 70 (C)41 : 70 (D 23 : 70

9. The solution of the differential equation 1 y2 x e t a n1

y dy

dx= 0 is

(A) x 2 = ket a n

1y (B)2xe

t a n1

y= e

2 t a n1

y k

(C)xet a n

1y

= t a n1

y k (D)xe2 t a n

1y

= et a n

1y k

SECTION II

Reasoning Type

This sect ion cont a ins 4 q uest ions numbered 10 t o 13. E ach q uest ion conta ins

STATEMENT 1 (Assertion) and STATEMENT 2 (Reason). Each question has 4 choices

(A), (B), (C) and (D), out of which ONLY ONE is correct.

(A) S t a t ement 1 is True, st a t ement 2 is True; st a tement 2 is a correctexpla na tion for sta tement 1.

(B) S t a tement 1 is True, st a tement 2 is True; st a tement 2 is not a cor rectexpla na tion for sta tement 1.

(C) St a tement 1 is True, sta tement 2 is False.

(D) St a tement 1 is False, sta tement 2 is True.




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SECTION III

Linked Comprehensive Type

Th is sect ion con ta in s 2 pa r a gr a ph s. B a sed u pon ea ch pa r a gr a ph , 3 mult iple ch oice

qu estions ha ve to be a nsw ered. E a ch quest ion h a s 4 choices (A), (B ), (C) an d (D), out ofw hich ONLY ONE is correct.

Paragraph for Question Nos. 14 to 16

Let O be t he or th ocen tr e. S in ce AD B C, B E C A, a n d

CF AB , th en OA BC , OB CA a nd OC AB .

Solving an y t w o of these, we can get coordina tes of O.

I f the sides of t he t r ia ngle a re given , t hen find t he

eq ua t ions of the line perpendicula r to t hese t wo sides a nd

pa s sin g t h rou gh t h e oppos it e v er t ices . S olv e t h ese eq u a t ion st o g et t h e coor din a t es of t h e or t hocen t re a n d cen t roid d iv id es

th e line joining t he orthocentre a nd circumcentre in th e ra tio 2 : 1.

14.The coordinates of the orthocentre of the triangle having vertices (0, 0), (2, 1) and(1, 3) a re

(A)1

5,

2

5(B)

3

5,

6

5(C)

6

5,

3

5(D)

2

5,

1

5

15.Th e coor din a tes of t he or th ocen tr e of t he t ria n gle for med by t he lin es xy = 0 a n d

y = 1 x are

(A)(0, 0) (B)(2, 1) (C)(2, 1) (D)(1, 2)

16. I f a t ria ngle h as it s ort hocen tre a t (2, 3) a nd circumcen tre a t5

6,

7

8, t hen the

coordina tes of the centroid of th e tria ngle is

(A)12

11,

9

19(B)

9

11,

12

19(C)

19

12,

11

9(D)

11

9,

19

12




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I nt egr a ls of t he for m f x , a x2 bx c dx ca n be eva lua ted w ith t he help ofthe E uler s substit utions. There a re norma lly 3 Eulers substitutions.

1. F irs t Eu ler s substitu tion: If a > 0, we put a x2 bx c = t x a

or a x2+ bx + c = t

2+ a x

22t x a or bx c = t

2 2t x a .

2. Second E uler s substit ution: If c > 0, we put a x2 bx c = t x c

or a x + b = t2x 2t c.

3. Th ir d E u ler s subst it ut ion : I f t he t rin omia l a x2

+ bx + c ha s rea l roots a nd

tha t i s ax2+ b x + c = a (x ) (x ), th en w e put a x

2 bx c = x t

or (x )t .

17.To eva lua te the integra l dxx 4x

2 2x 8

, a good substit ut ion is 4x2 2x 8 =

(A)t 4x (B)t 8x (C)t 2x (D)t 32x

18.The value of the integral

dx

x 1 x2 6x 5

is

(A)1

2

x 5

1 xC (B) 2

x 5

1 xC

(C)1 x

x 5C (D)

1

2

1 x

x 5 C




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PART B : PHYSICS

SECTION I


Th is sect ion con ta in s 9 m ult iple ch oice q uest ion s n um ber ed 23 t o 31. E a ch q uest ion

ha s 4 choices (A), (B), (C) a nd (D ), out of w hich ONL Y ONE is corr ect.

23.An a irplane is flying in a horizont a l circle a t a speed of 540 km/h. B a nked for th is

t urn , t he w ings of the pla ne a re t ilted a t a n a ngle 45 fr om t he h or izon ta l.

Assume t ha t a lift force a ct ing perpendicula r t o t he w ings holds t he a ircra ft in

th e sky. The ra dius of t he circle in w hich t he pla ne is flyin g is (Ta ke g = 10 m/s2

)

(A)1000 m (B)2250 m (C)500 m (D)4500 m

24.The ra t io of number of a toms of14

C t o12

C in living ma tter is mea sured to be

1.3 10 12

a t t h e pr es en t t im e. A 12 g s a mple of ca r bon pr od uces 180 d eca y s/m in

due to the small a mount of14

C in it. The ha lf-life of14

C is nearly

[1 year = 3.15 107s ]

(A)574 year s (B)5740 year s (C)2870 year s (D)287 year s

25.A r ocket is in ou ter spa ce, fa r fr om a n y pla n et , w h en t he r ocket en gin e is t ur ned

on . I n t he fir st secon d of fir in g, t he r ocket eject s 1

120of it s ma ss w it h a rela tive

speed of 2400 m/s. The r ocket s in it ia l a ccelera ti on is

(A)20 m /s2 (B)30 m/s

2 (C)40 m /s

2 (D)50 m/s

2




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26.Tw o sq ua r e con du ct in g pla t es w it h sides of len gt h L a r e sepa r a t ed by a dist a n ce

D . A dielect ric sla b w ith const ant k w ith dimensions L L D is insert ed a

dist a nce x in to t he spa ce bet w een t he pla t es. A con st a nt pot en tia l differ en ce V

betw een t he pla tes is ma in ta ined by connect ing a ba t t ery to the pla tes. I f t he

d ielect r ic is in ser ted a n a d dit ion a l d is ta n ce d x in t o t h e s pa ce bet w een t h e pla t es ,

th e cha nge in stored energy is

(A)

0V

2dx

2 (B)

k0

L2

V2

dx

2 D

(C)

k 1 0

L V d x

D (D)

k 1 0

V2

L dx

2 D

27.Tw o poin t ch a r ges q 1

= 2 C a nd q 2

= 2 C a re loca t ed a t x = 0, y = 0.3 m a nd

x = 0, y = 0.3 m respect ively . Th e n et elect ric force on a t hird poin t ch a rge

Q = 4 C a t x = 0.4 m, y = 0 is

(A)(0.46 N) i (B)(0.34 N) j

(C)(0.34 N) j (D)(0.46 N) i

28.A diverging lens a nd a n object a re posit ioned a s

sh ow n in t he Figure a t left . Which of t he ra ys a , b,

c a nd d could ema na te from poin t Q a t t he top of

t he object ?

(A)a , b and c (B)a a n d c

(C)a a nd b (D)a l l




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29.The int ensit y a t a ny poin t in t he interference pa ttern is I = I0

5

9

4

9cos ,

where is the pha se difference betw een the tw o w a ves a s mea sured a t a

pa rt icula r point on t he screen a nd I0

is t he ma ximum in tensit y in t he pa t tern .

Then t he ra tio of the a mplitud es of the w a ve from th e tw o slits is

(A)5

4or

5

4(B)

1

3or 3 (C)2 or

1

2(D)

1

5or 5

30.A pia n o t un er st ret ch es a st eel pia n o w ir e w it h a t en sion of 800 N. Th e st eel w ir eis 0.4 m long a nd ha s a ma ss 2 g. Th e number of t he highest ha rmonic t ha t could

be heard by a person w ho is ca pable of hea ring frequencies up to 104Hz is

(A)100 (B)150 (C)50 (D)20

31.Th e engine of a sport s ca r t akes in a ir a t 27C a n d 1 a t m os ph er e a n d com pr es ses

it a dia ba t ica lly t o 0.09 t imes t he origina l volume. The a ir ma y be t rea ted a s a n

idea l ga s w i th = 1.5. The fina l temperat ure of the ga s is

(A)1000 K (B)900 K (C)300 K (D)100 K

SECTION II

Reasoning Type


STATEMENT 1 (Assertion) and STATEMENT 2 (Reason). Each question has 4 choices(A), (B ), (C) a nd (D ), out of wh ich ONL Y ONE is corr ect.

(A) S t a t ement 1 is True, sta t ement 2 is True; st a tement 2 is a correctexplan a tion for sta tement 1.

(B) S t a tement 1 is True, sta tement 2 is True; st a tement 2 is not a cor rectexplan a tion for sta tement 1.






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32.Statement 1: Cy clotron frequ ency does n ot depend on speed of cha rged pa rticle

and

Statement 2: K in et ic en er gy of ch a r ged pa r t icle in cy clot r on is in depen den t of

its cha rge.

33.Statement 1: According t o Lenz s la w of electroma gnetic induction, t he inducede.m.f is in t he direction opposing t he cha nge in ma gnet ic flux

and

Statement 2: If t he flux is increa sing sod

B

dtis positive, th en th e induced e.m.f

or current is nega tive.

34.Statement 1: I n You ngs dou ble slit in terfer en ce pa t t er n t he fr in ge w id th is a

universal consta nt

and

Statement 2: The fringe w idth ca n be cha nged eit her by cha nging thewa velength or by cha nging the sepa ra tion between the tw o sli ts .

35.Statement 1: Th e a n gu la r momen tum of a n elect ron m ovin g in a st a ble orbita round t he nucleus is qua ntised

and

Statement 2: E ach elect ron in a n a tom w ill exist only w it h certa in specificva lue of energy.

SECTION III

Linked Comprehension Type

Th is sect ion con ta in s 2 pa ra gra ph s. B a sed u pon ea ch pa r agra ph , 3 mult iple ch oice

qu estions ha ve to be a nsw ered. Ea ch quest ion h a s 4 choices (A), (B ), (C) an d (D ), out of

w hich ONLY ONE is correct.




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An eleva t or of 2000 kg w it h broken ca bles is fa llin g a t 4 m/s a n d it is st opped by a

spring a t t he bot t om of the sha ft . The spring is supposed to st op the eleva tor ,

compressing 2 m. D uring t he mot ion a sa fety cla mp a pplies a consta nt 17000 N

frictiona l force to th e elevat or.

36. Init ia l tota l mecha nica l energy is

(A)21.2 103J (B)16 10

3J

(C)18 103J (D)16 10

3J

37.The force consta nt of the spring is n ea rly

(A)104N/m (B)10

3N/m (C)10

2N/m (D)10 N /m

38. I f t her e is n o sa fet y cla m p a t t he bot t om , t hen w h ich of t he follow in g st a t em en t iswrong ?

(A)There must be a n et upw a rd force 1600 N on th e eleva tor.

(B)The elevation would bounce back upward.

(C)There must be a net down w a rd force 1600 N on th e elevat or.

(D)There is no energy loss d ue t o frictiona l force.




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SECTION IV

Matrix-Match Type

Th is sect ion con ta in s 3 q uest ion s. E a ch q uest ion con ta in s st a temen ts given in t w o

column s w hich ha ve t o be ma tch ed. S ta temen ts (A, B , C , D ) in Column I ha ve t o bema tched w ith sta tement s (p, q , r , s) in Column II . Th e a n sw ers t o t hese q uest ion sha ve to be a ppropriat ely bubbled as illustra ted in th e follow ing example.

I f t he correct ma tches a re A-p, A-s, B -q , B -r , C -p, C -q a nd D -s, t hen t he correct ly

bubbled 4 4 ma trix should be as follows:

p q r s

A p q r s

B p q r sC p q r s

D p q r s

42. Column I Column II

(A) Electrosta tic field (p) Conservat ive field

(B) In duced electr ic field (q) Lin es of force open

(C) Magnetic field (r) Non -conservative field

(D) Electromagnetic field (s) Lin es of force closed


(A) A solid cylinder is rolling dow n (p) the frictional force is dissipative

a n inclined pla ne of inclina tion

(B) A block is sliding d own a n (q) t he frictiona l force is zero

inclined plane of inclination




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(C) A solid cylinder is r olling w ith out (r) th e frictiona l force w ill aidslipping in th e horizonta l surfa ce rota tion but hinder tra nsla tion

(D) A solid rin g is rolling on t he horizonta l (s) th e frictiona l force is cha nged ifsurfa ce a nd externa l force F is a pplied a ngle of plane is cha nged

a t th e topmost of a ring

44.A w ire a long t he x-a xis ca rr ies a current of 2 A in t he nega t ive direct ion . Th e

force on 1 cm section of th e wir e exert ed by t hese ma gnet ic fields

(a) B1

= 0.8 T j T,

(b) B2

= 0.2 i 0.3 j 0.3 k T

(c) B

3

= 0.8 j 0.4 k T

(d) B4

= 0.4 i T

are F1, F

2, F

3a nd F

4r espectively.

Then match Column I w ith th ose in Column II .

Column I Column II

(A) F

3

(p) 0.2 10 2

3 j 5 k

(B) F4

(q) 0.2 10 2

j 3 k

(C) Force due to a ll ma gnetic (r) 8 10 3

j 2 k N

fields B1, B

2, B

3and B

4, F

(D) Force due t o mag netic fields (s) zero

B1and B

2, F




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PART C : CHEMISTRY

SECTION I


Th is s ect ion con t a in s 9 m ult iple ch oice q u es tion s n um ber ed 45 t o 53. E a ch q u est ion

has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

45.The pH a t w hich Mg(OH )2

st a rt s precipit a t ing from a solut ion cont a in ing

1 10 3

M Mg2+

ions is (Ksp

Mg(OH )2= 1 10

11)

(A)3.8 (B)9.0 (C)6.9 (D)10

46. In a redox reaction one molecule of KN O3ga ins 3 electr ons. The product w ill be

(A)N O2 (B)N

2O

5 (C)N

2O (D)N O

47.C on sid er t h e r ea ct ion : 2N2O

5 4N O

2+ O

2. Th e r a te con st a n t for t he r ea ct ion

is 3.2 10 5

s 1

. The ra te of t he rea ct ion is 2.4 10 5

mol L 1

s 1

. Th e mola r

concentr a tion of N2O

5is

(A)0.875 (B)0.75 (C)0.4375 (D)0.375

48.The product P in th e rea ction, is

(A)(+ ) 2-B romosuccinic a cid (B)Meso-dibromosuccinic acid

(C)() Dibromosuccinic acid (D)() 2-B romosuccinic a cid




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49.(CH3)3C Mg B r + D

2O P roduct. The product is

(A)(C D3)3C OD (B)(C D

3)3C D

(C)(C H 3)3C D (D)(C H 3)3C OD

50.Nucleophilic a ddit ion is most fa voured in

(A)C H3C H O (B)C H

3C H

2C H O

(C) (D)

51.O3(I); N

O2(II ); CO

2(III); N

3

(IV)

Among th e a bove species, those ha ving similar sha pe are

(A)(I) an d (II ) (B)(II I) an d (IV)

(C)(I), (II ) an d (III ) (D)(II), (II I) a nd (IV)

52.The correct decreas ing order of bond energy a mong ha logens is

(A) F2> C l2> B r2> I2 (B)C l2> F2> B r2> I2

(C) C l2> B r

2> F

2> I

2 (D)C l

2> F

2> I

2> B r

2

53.The correct in crea sing order of bond a ngle is

(A) C lO2< OF

2< C l

2O < H

2O (B)C lO

2< C l

2O < H

2O < OF

2

(C) OF2< H

2O < Cl

2O < ClO

2 (D)OF

2< C l

2O < H

2O < ClO

2




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SECTION II

Reasoning Type


STATEMENT 1 (Assertion) and STATEMENT 2 (Reason). Each question has 4 choices

(A), (B ), (C) a nd (D ), out of wh ich ONL Y ONE is corr ect.

(A) Statement 1 is True, statement 2 is True; statement 2 is a correct explanationfor sta tement 1.

(B) S t a tement 1 is True, sta tement 2 is True; st a tement 2 is not a cor rectexplan a tion for sta tement 1.



54.Statement 1: The complex [Co(NH3

)6

]3+

w ill be pa ra ma gnetic.

and

Statement 2: Coba lt (Z = 27) ha s a n odd num ber of electrons in its dsub sh ell.

55.Statement 1: D urin g isot herma l expa n sion of a n idea l ga s in to va cuum, h ea ta bsorbed is zero.

and

Statement 2: Idea l ga s molecules occupy zero volume.

56.Statement 1: For ma ny rea ct ion s, t he ra t e of t he rea ct ion doubles for every

10C r ise of temperat ure.and

Statement 2: The energy of a ct iva t ion ra pidly decrea ses w it h rise oftemperature.

57.Statement 1: H y dr oly sis of R C l is slow but t a kes pla ce fa st er in presen ce of

a l i t t le qua nti ty of added KI.

and

Statement 2: I

is a wea ker nucleophile and a better leaving group tha n C l

.




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For the reaction, 2A + B22AB , the follow ing da ta w ere obta ined.

Experiment [A] mol L

1

[B2] mol L

1

Initial Rate

1 0.50 0.50 1.75 10 3

2 0.50 1.00 3.5 10 3

3 1.00 1.00 3.5 10 3

61.Order wit h respect t o A a nd B2a re, respectively

(A)2, 1 (B)1, 1 (C)0, 1 (D)1, 0

62.Ra te consta nt for the reaction is

(A)1.75 103

(B)3.5 103

(C)1.75 104

(D)3.5 104

63. In it ia l ra te if t he concent ra tion of A is 2 mol L 1

a n d con cen tr at ion of B2

is

2 mol L 1

i s

(A)3.5 103 (B)1.75 103 (C)7.0 103 (D)3.5 104

SECTION IV

Matrix-Match Type

Th is sect ion con ta in s 3 q uest ion s. E a ch q uest ion con ta in s st a temen ts given in t w o

column s w hich ha ve t o be ma tch ed. S ta temen ts (A, B , C , D ) in Column I ha ve t o bema tched w ith sta tement s (p, q , r , s) in Column II . Th e a n sw ers t o t hese q uest ion sha ve to be a ppropriat ely bubbled as illustra ted in th e follow ing example.




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I f t he correct ma tches a re A-p, A-s, B -q , B -r , C -p, C -q a nd D -s, t hen t he correct ly

bubbled 4 4 ma trix should be as follows:

p q r s

A p q r sB p q r s

C p q r s

D p q r s


(A) XeF4 (p)sp

3d

2

(B) I3

(q) sp

3d

(C) XeF2 (r) 2 lone pairs on centr a l a tom

(D) B rF4

(s) 3 lone pairs on centr a l a tom


(A) S O2a t 0 .5 a t m and 0C (p) Z 1

(B) NH3a t 0.001 a tm a nd 1000C (q) P(V nb) = nRT

(C) H e ga s a t P 0, 0C (r) S trong int ermolecular at tra ctive forces

(D) He gas a t P = 200 a t m, 0C (s) P V = n RT


(A) Sucrose (p)Glycosidic linkage

(B) Maltose (q) Reducing

(C) Starch (r) Non -reducing

(D) Protein (s) Na tura l polymer




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