iit 09 sts3 paper2 qns

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BRILLIA N TSHO M E BA SED FULL-SYLLA BUS SIM ULA TO R TEST SERIES

FOR OUR STUDENTSTOWARDS

IIT-JO INT EN TRA N C E EXA M INA TIO N , 2009

QUESTION PAPER CODE

Time: 3 Hours Maximum Marks: 243

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONS:

Name: . Enrollment No.:

Brilliant Tutorials Pvt. Ltd. IIT/STS III/MPC/P(II) - 1

3

A. General1. This booklet is your Question Paper containing 66 questions. The booklet has 24 pages.2. This question paper CODE is pr in ted on t he r igh t h an d t op cor ner of t his s heet a nd on t he ba ck pa ge

(pa ge no. 24) of th is booklet.3. This quest ion paper conta ins 1 blank pa ge for your rough w ork. No additiona l sheets w ill be provided for

rough work.4. B la n k pa p er s, clipb oa r ds , log t a bles , s lid e r ules , ca lcu la t or s, cellu la r ph on es , pa g er s a n d elect r on ic

gadgets in any form are not allowed to be carried inside the examination hall.5. F ill in t he boxes pr ovid ed below on t his pa ge a nd a ls o w r it e your Name a nd Enrollment No. in t he

space provided on the back page (page no. 24) of this booklet.6. The answer sheet, a machine -read able Objective Response S heet (ORS) , is provided separately.7. D O NOT TAMP ER WITH /MU TIL ATE THE ORS OR TH E B OOK LE T.8. Do not break the seals of the questions -paper booklet before being inst ructed t o do so by t he invigilators.

B. Filling the ORS9. On t he low er pa rt of t he ORS , w rit e in ink, your na me in box L1, your E nrollment No. in box L2 a nd

Nam e of th e Centre in box L3. Do not write these anywhere else .10. The ORS has a CODE printed on i ts lower and upper par ts .11. Ma ke sure t he COD E on t he ORS is t he sa me a s t ha t on t his booklet a nd put your signa ture in ink in

box L4 on the ORS affirm ing tha t you have verified this.12. IF THE COD ES DO N OT MATCH , ASK FOR A CH ANG E OF THE BOOK LET.

C. Question paper format: Read the inst ructions printed on t he back pa ge (page no. 24) of this booklet.D. Marking scheme: Read the inst ructions on the ba ck page (page no. 24) of this booklet.

S E A L

S E A L

D O

N O T B R E A K T H E S E A L S O N T H I S B O O K L E T , A W A I T I N S T R U C T I O N S F R O M

T H E I N V I G I L A T O R

MATHEMATICS PHYSICS CHEMISTRY

PAPER II

I have read all the instructionsand shall abide by them.

...............................................Signature of the Candidate

I have verified all the informationsfilled in by the Candidate.

...............................................Signature of the Invigilator

IIT-JEE 2009STS III/ M PC / P(II) / Q N S


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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 u mber ed 1 t o 9. E a ch q u es tion h a s4 choices (A), (B ), (C) a nd (D ), out of w hich O NLY ON E is corr ect.

1. Let f(x) = a x2 + b x + c, a 0 a nd f( 1) < 1, f(1) > 1 a nd f(3) < 4. Then

(A) a < 18

(B) b > 1 (C) a i s negat ive (D) b < 1

2. If Z = 2a sin (sin + i cos ), th en t he locus of Z is

(A) a circle wh ose cent re is a (B) a circle wh ose cent re is a

(C) a circle wh ose ra dius isa

2(D) a circle of ra dius 2a

3. In a AB C, th e minimum va lue of t a n2 A

2ta n

2 B

2t a n

2 C

2is equa l to

(A) 0 (B) 1

2(C) 1 (D) 3

4. In a AB C, coordina tes of A a re (4, 6), AB = 12 a nd B AC =

3. Th e m id poin t of

AC is (4, 12). Then the radius of the incircle of AB C is

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


SPACE FOR ROUGH WORK


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5. If t he position vectors of th e points A, B , C, D a re a , b , c , d and i fb c 2d b c = c a 2d c a = 0, then D is

(A) circumcentr e of AB C (B) incentr e of AB C

(C) orth ocent re of AB C (D) cent roid of AB C

6. An ordina ry die is rolled n t imes. Th e proba bility of get t ing a n odd number 3t imes is eq ua l to th e proba bilit y of get t ing a n even number 4 t imes. Th en th eproba bility of getting a n even num ber, even num ber of times is

(A) 63

128(B)

1

4(C)

1

8(D)

1

2

7. The doma in of th e function f x = 2 log1 2 x log 1 2 x

2

15 is

(A) 1

32, 8 (B) 0 ,

1

32(C) (0, 8] (D) (0, 5]

8. Let ddx

F x = es in x

x, x > 0 . I f

1

4

2es in x

2

xdx = F(k) F(1), t hen one of th e

possible va lues of k is

(A) 4 (B) 4 (C) 16 (D) 8

9.

2

cot1

cot x dx is

(A) 22 (B) 32 (C) 3

2

2(D) 92




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SECTION II

Reasoning Type

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

STATEMENT 1 (Assertion) and STATEMENT 2 (Reason). Each question has 4 choices(A), (B), (C) a nd (D ), out of w hich ON LY ONE is corr ect.

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

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

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

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

10.Statement 1: I f a b , b c , c a a re n on -copla n a r , t h en a , b , c a re non -coplanar

and

Statement 2: a b b c c a = 2 a b c .

11.Statement 1: p cos x q sin x = r ha s a solution only if r p2

q 2

and

Statement 2: sin = c has a solution only if 1 c 1.12.Statement 1: Area bet w een t he curves y = e x, y = loge x, x + y = 1, x + y = 2

is eq ua l to t w ice t he a rea betw een y = ex, y = x, x + y = 1 a nd

x + y = 2

and

Statement 2: The curves y = e x a nd y = loge x a r e sy mm et rica l w it h r espect t o

the l ine y = x.




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13.Statement 1: The num ber of terms in t he expa nsion of (x + y + z) 25 is 351

and

Statement 2: The nu mber of terms in t he expa nsion of (x + y) n is (n + 1).

SECTION II I

Linked Comprehension Type

Th is sect ion con ta in s 2 pa r a gr a ph s. B a s ed u pon ea ch pa r a gr a ph , 3 mult iple ch oicequ estions h a ve to be a ns w ered. Ea 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

50 objects a 1, a 2, a 3, ..., a50 are ar ra nged in a row.

14. The n umber of wa ys of selecting tw o of th e objects s o tha t th ey a re not consecutiveis

(A) 1176 (B) 1175 (C) 1225 (D) none of these

15. Number of w a ys of forming t hree element subset s in w hich exa ct ly t wo of th eelements are consecutive

(A) 2266 (B) 2302 (C) 2256 (D) none of th ese

16. Number of t hree element subset s w it h the condit ion no tw o subset s h ave thesame pair of consecutive elements

(A) 19600 (B) 17296 (C) 17388 (D) 17344


Let y = 2x4 x2 be the equa tion of a curve.

17. The equa tion of the norma l at th e origin is

(A) y = 0 (B) x = 0 (C) not unique (D) none of th ese

18. The depth of th e low est point on th e cur ve below th e x -a xis is

(A) 1

8(B)

1

4(C)

1

16(D) none of th ese




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19. The a rea betw een t he curve an d t he x -a xis is

(A) 1

15(B)

1

15 2(C) 2 2

15(D) 2

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SECTION IVMatrix -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 ocolumn s w h ich h a ve t o be ma t ch ed. S ta t emen ts (A, B , C , D ) in Column I ha ve t o bema tched w ith sta t ement s (p, q , r , s) in Column II . Th e a n sw er s t o t hese q uest ion sha ve to be appropria tely bubbled a s illustr a ted in th e follow ing example.

I f t h e correct ma tches a re A -p, A-s, B -q , B-r , C -p, C -q a n d D -s, t hen t he cor rect lybubbled 4 4 mat rix should be a s follow s:

p q r sA p q r s

B p q r s

C p q r s

D p q r s

20. Column I Column II

(A) cos2

7cos

4

7cos

6

7 (p) 1

8

(B) cos

9sin

5

18cos

3

9sin

18(q)

1

16

(C) sin

14sin

3

14sin

5

14sin

21

14(r) 1

8

(D) sin

15sin

3

10sin

4

15(s) 1

2




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(A) The integer just gr eat er tha n 3 16

is (p) 723

(B) The int eger just less t ha n 2 35

is (q) 416

(C) The nu mber of na tur a l numbers from 2 to 999 (r) 720w hich ha ve none of the digits repea ted is

(D) The num ber of w a ys 5 different red flow ers a nd (s) 7373 different w hite f low ers ca n be ar ra nged in aga rlan d so tha t no tw o w hite f low ers are together is


(A) 1

1

1 2x3

x2

1 2x3

x2

dx (p)56

15

(B) 0

1

x 1 x4

dx (q)1

2

(C)

8

0

2

cos x

2dx (r)

1

30

(D) 4

4

1

cos6

xdx (s) 0




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PART B : PHYSICS

SECTION I

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

23. Ch oose the incorrect s ta tement .

(A) A dimensiona lly correct equa tion ma y be correct.

(B) A dimensiona lly correct equa tion ma y be incorrect.

(C) A dimensiona lly incorrect equa tion ma y be correct.

(D) A dimensiona lly incorrect equa tion ma y be incorrect.24. A pa rt icle moves in t he x -y pla n e w it h velocit y v = a i bx j , w here a a n d b a re

consta nt s. Initia lly, the part icle w a s a t th e origin. The tra jectory of th e pa rt icle is

(A) (B)

(C) (D)




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25. Tw o solid bod ies r ot a t e a b ou t st a t ion a r y m ut ua lly per pen dicu la r in ter sect in ga xes w it h con st a nt a n gula r velocit ies 1 a nd 2. Wha t is the ma gn itude of

a ngula r velocity of one w ith r espect t o the oth er?

(A) 1 2 (B) 12

22

(C) 12

22

(D) 1 + 2

26. In Figure s h ow n , f in d t h e m a g n it u de of a cceler a t i onof m, given t ha t t he st r in g is inext ensible a nd

m a ssless a n d t h e a cceler a t ion of M is 2 m /s2

t owardsleft.

(A) 2 3 m s2

(B) 3 2 m s2

(C) 4 2 m s2

(D) 2 5 m s2

27. A pa r t icle h a vin g ch a r ge t o m a ss r a t ioq

m= k is project ed in a

ma gn et ic field B w ith a speed v = 2kB d a s sh ow n in Figure ,w here d is th e w idt h of th e region in w hich ma gn et ic field ispresent . For th is s itua t ion, ma rk the incorrect s ta tement .

(A) P a rt icle rema ins in th e magn etic field for a time of 6kB

(B) I t t ra vels a dista nce of d

3in th e magn etic field

(C) The angle of deviation from its initial direction is 30 .

(D) The displa cement of pa rt icle in ma gnet ic field is 2d sin 15 .




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28. Two plane mirrors are placed as shown in Figure .A point object O is approaching the intersectionpoin t A of mirrors w it h a speed of 100 cm/s. Th evelocit y of im a ge of t he object for med by M 2 wi th

r es pect t o v elocit y of im a ge of object for med by M 1is

(A) 128 i 96 j cm s

(B) 28 i 48 j cm s

(C) 128 i 48 j cm s

(D) 100 i 48 j cm s

29. S ome ca ses a r e given below. I den tify t he ca se in w h ich t he emf is in duced , w h ena uniform ma gnetic field B is applied, thr oughout.

(A) In (I), (II I) a nd (IV) only (B) In (II ), (II I) a nd (IV) only

(C) In (II I) only (D) In a l l the four

30. A poin t source of ligh t of pow er P a nd w avelen gth is emit t ing ligh t in a lld irect ion s. Th e n umber of ph ot on s presen t in a sph er ica l region of ra dius r t ora dius 2r with centre a t source, is

(A) P

4 r2

h c

(B) P r

h c2

(C) P

4 r h c2

(D) P

hc




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31. Du ring t he process A -B for a n idea l ga s

(A) Work done on t he ga s is zero

(B) Density of the gas is consta nt

(C) S lope of lin e AB fr om t he T -ax i s i s d irect ly propor t iona lto th e number of moles of the ga s

(D) All of the a bove

SECTION II

Reasoning Type

This sect ion con t a ins 4 q uest ions numbered 32 t o 35. E ach q uest ion con ta insSTATEMENT 1 (Assertion) and STATEMENT 2 (Reason). Each question has 4 choices(A), (B), (C) a nd (D ), out of w hich ON LY ONE is corr ect.

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




32.Statement 1: I nt ern a l forces of t he bra ke of a veh icle, ca n br in g t he cen tre ofma ss of the vehicle to rest

and

Statement 2: I f Fext = 0, t he cen t re of ma ss keeps on movin g w it h const a nt

velocity.

33.Statement 1: Th e differen t ser ies of emission spect ra (like Lyma n , B a lmeretc.,) of a tomic hy drogen ga s a re produced by different a toms

and

Statement 2: A sample of atomic hydrogen gas consists of millions of atoms.




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34.Statement 1: An in duct or a n d a ca pa cit or con nect ed in t he cir cuit sh ow n inFigure . The a mmeter ma y rea d infini ty.

and

Statement 2: At resona nce, volta ge in coil a nd ca pa cita nce a re equa l an d out ofpha se by 180 .

35.Statement 1: Na rrow er th e open orga n pipe, higher w ill be the pitch

and

Statement 2: The frequ ency of open orga n pipe depend s on its ra dius.

SECTION II I


Th is sect ion con ta in s 2 pa r a gr a ph s. B a s ed u pon ea ch pa r a gr a ph , 3 mult iple ch oicequ estions h a ve to be a ns w ered. Ea ch quest ion h a s 4 choices (A), (B ), (C) an d (D ), out ofw hich ONLY ONE is correct.


Tw o circula r loops of ra dii R 1 a nd R 2 a re pla ced

coa xia lly a s sh ow n in Figure . From t ime per iod t < 0, theloop 1 ca r r ies st ea d y cu rr en t I 0 w h ile loop 2 d oes n ot ca r ry

a n y curr en t. Th en loop 1 is discon nect ed from it s pow ersource a t t = 0 a nd curren t ca rr ied by it deca ys t o zero ina n expon en tia l ma n ner . As a r esult of w h ich flux lin ked w it h loop 2 d eca y s a n d h en cea n in duced current flow s t hrough th e second loop.

Take R 1 >> R 2 a nd consider only mu tua l induction effects M betw een t he coils.




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36. The coefficient of mut ua l indu cta nce M betw een tw o coils is

(A)

0

2R

1

2R

2

2

2 R12 b2

3 2(B)

0 R

1

2

2R2

(C)

0 R

2

2(D)

0 R

1

2R

2

2

2 R1

2b

23 2

37. Th e t ot a l ch a rge ca r ried by in duced cur ren t in loop 2 is given by (w h er e R is t heresist a nce of loop 2)

(A) MI

0

R(B)

2MI0

R(C)

MI0

2R(D) none of th ese

38. The curr ent in loop 2 as a fun ction of time is given by

(A) I0e

M

Rt

(B) I0

e

R

Mt

(C) I0e Mt

(D) I0e Rt


A solid cylinder of ma ss M a nd ra dius R is a llow ed t oroll on a w edge of ma ss m w hich in t urn is kept on a smoot hhorizontal floor. The cylinder is rolling without slipping.

G iven x =cos

2 sin 2

2 2 s in2

39. The a ngula r a ccelera tion of cylinder is

(A) g sin x

R(B)

2g sin

3Rx (C)

2g cos x

3R(D)

2g s in

3R




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40. The frictiona l force betw een cylinder a nd w edge is

(A) Mg sin

3 x (B) Mg sin (C) Mg sin

2 sin2

x (D)

Mg sin

2 sin2

41. The norma l conta ct force betw een w edge an d ground is

(A) (2 mg cos ) x (B) mg cos

(C) 2 m g cos

2 sin2

(D) (mg cos ) x

SECTION IV

Matrix -Match Type



p q r s

A p q r s

B p q r s

C p q r s

D p q r s

42. Mat ch t he entr ies in Column I w ith t hose in Column II .

Column I Column II

(A) Longitudina l s tress (p) Volume changes

(B) Shear s t ress (q) Shape changes




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PART C : CHEMISTRY

SECTION I

Straight Objective Type

Th is sect ion con ta in s 9 m ult iple ch oice q uest ion s n um ber ed 45 t o 53. E a ch q uest ionha s 4 choices (A), (B ), (C) a nd (D ), out of w hich ON LY ONE is corr ect.

45. Ra tio of ra dii of second orbit of protium (H ), deut erium (D) an d t rit ium (T) is

(A) 1 : 2 : 3 (B) 12 : 22 : 32

(C) 1

12

: 1

22

: 1

32

(D) 1 : 1 : 1

46. Identify the incorrect s ta tement :

(A) Among th e ha lides, I is the most pow erful reducing a gent.

(B) Fluor ine does not show + 7 oxida t ion st a t e but iodin e sh ow s + 7 oxida t ions ta te .

(C) HOCl is s t ronger a cid tha n H OBr.

(D) HF is st ronger a cid tha n H Cl .

47. The meta l w hich ca nn ot be extra cted by smelting process is

(A) lead (B) copper (C) zinc (D) aluminium48. Which is t he false statement about orthoboric acid?

(A) I t is a s trong tr ibasic acid.

(B) I t does n ot a ct a s a pr ot on don or but beh a ves like a Lew is a cid by a ccept in g

OH

ion.

(C) It is prepar ed by the a ction of minera l acid on bora x solution.

(D) I t h a s a la yer structure in wh ich hyd rogen bonds unite B (OH) 3 units .




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49. Du ring debromina tion of meso -2, 3 -dibromobuta ne, th e ma jor product formed is

(A) CH 3 CH 2 C CH (B) CH 3 C C C H 3

(C) (D)

50. Identify the correct s ta tement :

(A) Ca rboca tions are pyra midal .

(B) Eth yl ca rbanion is p la na r.

(C) C6

H5

CH2

ion is pyra midal .

(D) Singlet carbene is diama gnetic.

51. In t he rea ct ion A + B C + 2D , tw o moles of A a nd t w o moles of B a re mixedin a volume of on e lit re. I f 1.2 moles of C is formed a t eq uilibr ium, t he va lue ofequilibrium const a nt is

(A) 1.69 (B) 1.08 (C) 10.8 (D) 16.9

52.

The products fina lly formed in th e a bove sequence of reactions a re

(A) C H 3CHO and CH 3COCH 3

(B) C H 3CH O and (CH 3C O)2O

(C) C H 3COCH 3 a nd (CH 3CO)2O

(D) C H 3CH 2C H O a n d C H 3COCH 3




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53. Th e solu bilit ies of ca r bon a t es d ecr ea s e d ow n w a r d in m a gn esiu m gr ou p d ue t o adecrease in

(A) hy dra tion energies of ca tions

(B) inter -ionic a tt ra ction(C) entr opy of solution forma tion

(D) lattice energies of the solids

SECTION II

Reasoning Type

This sect ion con t a ins 4 q uest ions numbered 54 t o 57. E ach q uest ion con ta insSTATEMENT 1 (Assertion) and STATEMENT 2 (Reason). Each question has 4 choices(A), (B), (C) a nd (D ), out of w hich ON LY ONE is corr ect.

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




54.Statement 1: C a r o s a cid is a stronger oxidising a gent th a n sulphuric a cid.

and

Statement 2: Oxid a t ion st a t es of su lph ur in C a r o s a cid a n d sulph ur ic a cid a r e+ 7 and + 6 respectively.

55.Statement 1: Oxida tion of a minona phtha lene yields phth a lic acid.

and

Statement 2: An a min o group a t ta ch ed t o ben zen e r in g ma kes it sen sit ive t ooxidation.




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56.Statement 1: When ch lorobenzene is t rea ted w ith a mmonia ga s, a niline isformed a t 80 C a nd one at mospheric pressure.

and

Statement 2: Ammonia is a str onger n ucleophile tha n chloride ion.

57.Statement 1: The chemica l equilibrium is dyn a mic in na tur e.

and

Statement 2: Th e r a te con st a nt s of for w a rd r ea ct ion a n d it s r ever se r ea ct iona re the same a t equil ibrium.

SECTION II I


Th is sect ion con ta in s 2 pa r a gr a ph s. B a s ed u pon ea ch pa r a gr a ph , 3 mult iple ch oicequ estions h a ve to be a ns w ered. Ea 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. 58 to 60

C a rbon yl group in a ldeh ydes a n d ket on es un dergo a ddit ion rea ct ion a s w ell a scon densa t ion rea ct ion . group is pola r in na t ure a nd h en ce it is a t t a cked byn ucleoph iles. I n t hese r ea ct ion s a ld eh ydes a r e more r ea ct ive t ha n ket on es. S ter iceffects a nd pola r effects decide th e reactivity of carbonyl gr oup.

58.

Th e produ ct is

(A)

(B)




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(C)

(D)

59. Consider t he following sequence of r eactions.

The fina l product N is

(A) (B)

(C) (D)

60. E nolisa tion is ma ximum in the ca se of

(A) (B) (C) (D)

Paragraph for Question Nos. 61 to 630.02 M a queous solut ion of NH 4Cl un dergoes hydrolysis. As a result of it , t h e

solution develops acidity.

NH4

+ H2O NH 4OH + H




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21

Th e ba s icit y con st a n t K b for NH 4OH is 1.85 105

a n d t he ion ic pr od uct of w a t er

Kw = 1 1014

a t 298 K. [pK b = 4.73]

61. F or t h e r ea ct ion , NH4

+ H2O NH 4OH + H. Th e h yd roly tic con st a nt of

NH4

ion is

(A) 5.4 1010

(B) 4.5 10 10 (C) 1.85 109

(D) 1.85 10 9

62. The degr ee of hy drolysis in th e a bove NH 4Cl solution is

(A) 5.0 103

(B) 1.64 10 4

(C) 5.0 104

(D) 1.64 10 5

63. The pH of 0.02 M a qu eous s olut ion of NH 4Cl is

(A) 4.52 (B) 4.48 (C) 5.48 (D) 5.52

SECTION IV

Matrix -Match Type



p q r s

A p q r s

B p q r s

C p q r s

D p q r s




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64. Column I Column IISpecies Nature of central atom

(A) B Cl3 (p) Formal charge = 0

(B) NH 3 (q) Formal cha rge = + 1

(C) NO 2 (r) Oxidation number = 3

(D) NH4

(s) Hy bridisa t ion: sp 2


(A) CO < CO2

iit 09 sts3 paper2 qns

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