iit jee mains question paper (10!04!2016) - xi

7/26/2019 IIT JEE Mains Question Paper (10!04!2016) - XI

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J E E M a i n s

PHYSICS, CHEMISTRY & MATHEMATICS

Time : 3 Hours Date : 10.04.2016 Maximum Marks - 360

INSTRUCTIONS

1. Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball Point Pen. Use ofpencil is strictly prohibited.

2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take

out the Answer Sheet and fill in the particulars carefully.3. The test is of 3 hoursduration.4. The Test Booklet consists of 90 questions. The maximum marks are 360.5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics

having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks forcorrect response.

6. Candidates will be awarded marks as stated above in instruction No. 5 for correct response of eachquestion. 1 (one) marks will be deducted for indicating incorrect response of each question. No deductionfrom the total score will be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in any questionwill be treated as wrong response and marks for wrong response will be deducted accordingly as perinstruction 6 above.

8. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side-1and Side-2of the Answer Sheet. Use of pencil is strictly prohibited.

9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobilephone, any electronic device, etc. except the Admit Card inside the examination room / hall.

10. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This spaceis given at the bottom of each page and in onepage (i.e. Page 20) at the end of the booklet.

11. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty inthe Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.

12. Do not fold or make any stray mark on the Answer Sheet.

Name of the Candidate (in Capital letters) : ________________________________________________

Roll Number : in figures

: in words ____________________________________________________________

Examination Centre Number :

Name of Examination Centre (in Capital letters) :____________________________________________

Candidates Signature : ___________________ 1. Invigilators Name : __________________

2. Invigilators Signature : __________________

IIT JEE Adv. XI Batches


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2KALRASHUKLA IIT JEE ADVANCED

Space for rough work.......................................................................................................................................................

SECTION 1 : PHYSICS

1. In the figure shown water is filled in symmetrical container. Fourpistons of equal areaAare used at the four opening to keep thewater in equilibrium. Now an additional force Fis applied at

each piston. The increase in the pressure at the centre of thecontainer due to this addition is

F2

F4

F3F1

(1)F

A(2)

2F

A

(3)4F

A(4) 0

2. The cubical containerABCDEFGH which is completely filled with an ideal (nonviscous and

incompressible) fluid, moves in a gravity free space with an acceleration of0

( ) a a i j k

wherea0is a positive constant. Then the only point in the container where pressure is maximum, is

A

B C

D

GF

E H

Y

Z

X

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

3. The density of ice isxgm/cc and that of water isygm/cc. What is the change in volume in cc,when mgm of ice melts ?(1) m(yx) (2) (yx)/m (3) mxy(x y) (4) m(1/y 1/x)


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4. Two identical cylindrical vessels with their bases at the same level, contain same liquid of density.The height of the liquid in one vessel ish

1and that in the other vessel inh

2. The area of either base

isA. The work done by gravity in equalizing the levels when the two vessels are connected is

(1) (h1 h

2)g (2) (h

1 h

2)gA (3)

21 2

1( )

2 h h g (4)

21 2

1( )

4 h h g A

5. A vessel with water is placed on a weighing pan and it reads600 g. Now a ball of mass 40 g and density 0.80 g cm3issunk into the water with pin of negligible volume, as shown infigure keeping it sunk. The weighing pan will show a reading :

Weighing pan(1) 600 g (2) 550 g(3) 650 g (4) 632 g

6. A small uniform tube is bent into a circular tube of radiusRandkept in the vertical plane. Equal volumes of two liquids ofdensities and (> ) fill half of the tube as shown. is the

angle which the radius passing through the interface makes withthe vertical.

OR

(1) 1tan

(2) 1tan

(3) 1tan

(4) 1tan

7. A particle performing SHM is found at its equilibrium at t= 1 sec. and it is found to have aspeed of 0.25 m/s at t= 2 sec. If the period of oscillation is 6 sec. Calculate amplitude ofoscillation

(1)3

m2

(2)3

m4

(3)6

m

(4)3

m8


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8. The angular frequency of motion whose equation2

24 9 0

d yy

dtis

(y= displacement and t= time)

(1)9

4(2)

4

9(3)

3

2(4)

2

3

9. A particle executes SHM with time periodTand amplitudeA. The maximum possible average

velocity in time4

Tis

(1)2A

T(2)

4A

T(3)

8A

T(4)

4 2A

T

10. Two pendulums have time periods Tand 5T/4. They start SHM at the same time from themean position. After how many oscillations of the smaller pendulum they will be again in thesame phase

(1) 5 (2) 4 (3) 11 (4) 9

11. A body performs simple harmonic oscillations along the straight lineABCDE with Cas themidpoint ofAE. Its kinetic energies atBandDare each one fourth of its maximum value. IfAE = 2R, the distance betweenBandDis

A B C D E

(1)3

2

R(2)

2

R(3) 3 R (4) 2 R

12. A particle starts oscillating simple harmonically from its equilibrium position then, the ratio ofkinetic energy and potential energy of the particle at the time T/12 is : (T: time period)(1) 2 : 1 (2) 3 : 1 (3) 4 : 1 (4) 1 : 4


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13. In the figure, the block of mass m, attached to the spring of stiffness kis in contact with thecompletely elastic wall and the compression in the spring is e. The spring is compressedfurther by e by displacing the block towards left and is then released. If the collision betweenthe block and the wall is completely elastic then the time period of oscillations of the block willbe

Wall

m

(1) 23 m

k(2) 2 m

k

(3)3

mk

(4)6

mk

14. A mass m, which is attached to a spring with spring constant k, oscillates on a horizontal table,

with amplitudeA. At an instant when the spring is stretched by 3 / 2,A a second mass mis

dropped vertically onto the original mass and immediately sticks to it. What is the amplitude ofthe resulting motion ?

(1)3

2A (2)

7

8A (3)

13

16A (4)

2

3A

15. A child with mass mis standing at the edge of a disc with moment of inertiaI, radiusRand initialangular velocity , See figure, the child jumps off the edge of the disc with tangential velocity vwith respect to the ground. The new angular velocity of the disc is

(1)2 2 I mvI

(2)2 2 2( ) I mR mvI

v

(3) I mvRI

(4)2( ) I mR mvRI


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16. A right triangular plateABCof mass mis free to rotate in the verticalplane about a fixed horizontal axis throughA. It is supported by astring such that the sideABis horizontal. The reaction at the supportAin equilibrium is

A l

l

C

B

(1)3

mg(2)

2

3

mg

(3)2

mg(4) mg

17. A mass mis moving at speed vperpendicular to a rod of length dand massM= 6mwhichpivots around of frictionless axle running through its centre. It strikes and sticks to the end of therod. The moment of inertia of the rod about its centre isMd2/12. Then the angular speed of thesystem right after the collision is(1) 2v/d (2) 2v/(3d) (3) v/d (4) 3v/(2d)

18. A block is projected upwards on an inclined plane of inclination 37 along the line of greatestslope of = 0.5 with velocity of 5 m/s. The block 1ststops at a distance of ______________from starting point(1) 1.25 m (2) 2.5 m (3) 10 m (4) 12.5 m

19. A block of mass mis hung vertically from an elastic thread of force constant mg/a. Initially thethread was at its natural length and the block is allowed to fall freely. The kinetic energy of theblock when it passes through the equilibrium position will be(1) mga (2) mga/2 (3) zero (4) 2mga

20. A particle is released from rest at origin. It moves under influence of potential field U=x2 3x.

Kinetic energy atx= 2 is(1) 2 J (2) 1 J (3) 1.5 J (4) 0 J


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21. A man of massMstands at one end of a plank of lengthLwhich lies at rest on a frictionless

surface. The man walks to other end of the plank. If the mass of the plank is ,3

Mthen the

distance that the man moves relative to ground is

(1)

3

4

L

(2) 4

L

(3)

4

5

L

(4) 3

L

22. A ball is projected from pointAwith a velocity 10 m/sperpendicular to the inclined plane as shown in figure.Range of the ball on the inclined plane is

30

A

(1)40

3m (2)

20

13m

(3)13

20m (4)

13

40m

23. BlockBof mass 100 kg rests on a rough surface of friction coefficient = 1.3. A rope is tiedto blockBas shown in figure. The maximum acceleration with which boyAof 25 kg can climbson rope without making block move is

37

100 kg

B

= 1/3

A

25kg

(1)4

3

g

(2)3

g

(3) 2

g

(4)3

4

g


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24. The graphs below show angular velocity as a function of time. In which one is the magnitude ofthe angular acceleration constantly decreasing ?

(1)

t

(2)

t

(3)

t

(4)

t

25 A particle is moving along the circlex2+y2= a2in anticlockwise direction. Thex-yplane is arough horizontal stationary surface. At the point (acos , asin ), the unit vector in the directionof friction on the particle is

(1) cos sin i j (2) (cos sin ) i j

(3) sin cos i j (4) cos sin i j

26. The work done by the force 2 2 F x i y j around the path

shown in the figure is

Y

B(a, a)

(a, 0)AO

(0, 0)

(0, a)C

X

(1)32

3a (2) zero

(3) a3 (4)34

3a

27. The figure shows a uniform rod lying along thex-axis. The locus of allthe points lying on thexy-plane, about which the moment of inertia of

the rod is same as that about Ois

y

xO

(1) an ellipse (2) a circle(3) a parabola (4) a straight line


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28. A rod is hinged at its centre and rotated by applying a constant torque starting from rest. Thepower developed by the external torque as a function of time is

(1)

Pext

time

(2)

Pext

time

(3)

Pext

time

(4)

Pext

time

29. A ladder of lengthLis slipping with its ends against a vertical wall and a horizontal floor. At acertain moment, the speed of the end in contact with the horizontal floor is vand the laddermakes an angle = 30 with the horizontal. Then the speed of the ladders center must be

(1)2

3

v(2)

2

v(3) v (4) None

30. A uniform circular disc placed on a rough horizontal surface has initially a velocityv0and an

angular velocity 0as shown in the figure. The disc comes to rest after moving some distance

in the direction of motion. Then 0

0v

ris

0

v0(1)

1

2(2) 1

(3)3

2(4) 2


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SECTION 2 : CHEMISTRY

31. The number of water molecules present in 0.20 g sample of CuSO4.5H

2O

(Molar mass = 249.7) is(1) 1.2 1021 (2) 2.14 1021 (3) 2.14 1022 (4) 1.2 1023

32. The group that has the species correctly listed in the order of decreasing radius is(1) Cu+2> Cu+> Cu (2) V > V+2> V+3

(3) F> Br> I (4) B > Be > Li

33. The number of isomers of dibromobiphenyl is(1) 8 (2) 10 (3) 12 (4) 14

34. The enthalpies of decomposition of methane and ethane are 400 and 670 kJ/mol resp. TheH

C Cin kJ/mol is

(1) 270 (2) 70 (3) 200 (4) 240

35. For the reaction3 2 5PCl (g) Cl (g) PCl (g) Kc is 26 at 250C. Kpat the same

temperature is(1) 4.6 103 (2) 5.7 103 (3) 6 101 (4) 6 103


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36. The correct product of the reactionO

is

(1)

O

(2)O

(3)

O

(4)O

37. According to VSEPR theory the shape of IF5molecule will be

(1) tetrahedral (2) trigonal bipyramidal(3) square pyramid (4) trigonal planar

38. The formal charges on the atoms underlined are respectively : 6 5C H C N O

(1) 0, 1, +1 (2) 1, +1, 1 (3) 0, +1, 1 (4) +1, 0, 1

39. The compound that does not have a bond is(1) SO

2(2) SF

6(3) O

2(4) SO

3

40. The number of valence electrons in an atom with the configuration 1s22s22p63s23p2is(1) 6 (2) 5 (3) 4 (4) 2

41. When 0.1 M NaOH is added to 0.1 dm3

of 0.1 M acetic acid the pH

is found to be 4.74.Given Ka = 1.8 105of the acid what fraction of the acid has been neutralised ?(1) quarter (2) half (3) three quarter (4) full


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42. The compound in which Mn has oxidation state of +3 is(1) KMnO

4(2) K

2[Mn(CN)

6]

(3) MnSO4

(4) CsMn(SO4)

212H

2O

43. The correct order of dipole moment is

(I)

OH

(II)

ClCl

(III)

CH3CH3

(1) I = II = III (2) I < II < III (3) I > II > III (4) II > I > III

44. The order of acidities of H-atoms underlined in the following compounds is in the order

(I) 2 3Ph CH CH (II) Ph C CH

(III) 2Ph CH CH (IV) CH2

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

45. The COC bond angle in dimethyl ether is(1) 90 (2) 110 (3) 120 (4) 180

46. The compound that is chiral is(1) 3-methyl-3-hexene (2) 4-chloro-1-methylhexane(3) 2-phenylpentane (4) 1,3-diisopropylbenzene

47. A beaker is heated from 27C to 127C. The % of air originally present in beaker that isexpelled is(1) 50% (2) 25% (3) 33% (4) 40%


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48. The IUPAC name of the following compound isO

O

OEt

(1) 3-methoxyethylpropanoate (2) ethyl-4-methoxybutanoate(3) 1,4-diethoxybutane (4) ethoxy-3-methoxybutyrate

49. The wavelength of a moving body of mass 0.1 mg is 3.31 1029m. The kinetic energy of thebody in J would be(1) 2 106J (2) 1 103J (3) 4 103J (4) 2 103J

50. The following titration curve represents the titration of a____________ acid with a ____base

1

pH

mL added

13

7(1) strong, strong(2) weak, strong(3) strong, weak(4) weak, weak

51. The element with the lowest electronegativity is(1) S (2) I (3) Ba (4) Al

52. The number of stereoisomers of compound CH3CH = CH CH(Br)CH

3is

(1) 2 (2) 3 (3) 4 (4) 6

53. Ka for HOCl is 3 108. Hence for the reaction2OCl H O HOCl OH

the Khwill be(1) 3.3 107 (2) 3 108 (3) 3 106 (4) 3.3 107

54. pHof a 0.2 M solution of Ca(OH)2will be

(1) 13.3 (2) 13.6 (3) 0.4 (4) 0.7


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55. The molarity of pure water is(1) 11.11 M (2) 22.22 M (3) 44.44 M (4) 55.55 M

56. ClOdisproportionates to 3ClO and Clin the proportion of

(1) 2 : 1 (2) 1 : 2 (3) 2 : 3 (4) 3 : 2

57. In the reaction : 2 2 22H S SO 3S 2H O the oxidizing agent is

(1) H2S (2) SO

2(3) S (4) H

2O

58. What is the w in the process shown for which the productPv is constant ?

10

1

1 10V(L)

P(atm)(1) 23 J

(2) 23 L-atm(3) 23 cal

(4) 23 erg

59. Tyres of large cargo planes are inflated with which gas ?(1) H

2(2) He (3) CO

2(4) N

2

60. The element that has the highest ionization energy from the following is(1) Na (2) K (3) Sc (4) Cs


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SECTION 3 : MATHEMATICS

61. In ,ABC if cos 2cos cos 2A B C then , ,a b c are in(1) A.P (2) H.P (3) G.P. (4) A.G.P

62. In ,ABC AD is the altitude fromA. If 2 2, 23 , abc

b c C AD b c then B

(1) 67 (2) 113 (3) 73 (4) 46

63. If the medianADof ABC, makes an angle withABthen sin (A ) =

(1)sinbc

(2)sincb

(3)sina

c(4)

sinc

b

64. In triangleABCsinA, sinBand sin Care in A.P., then(1) the altitudes are in H.P. (2) the altitudes are in A.P.

(3) the altitudes are in G.P. (4) none of these

65. In triangleABC, a2+ c2= 2002b2, thencot cot

cot

A CB

is equal to

(1)1

2001(2)

2

2001(3)

3

2001(4)

4

2001

66. The number of ways of permuting the letters of the word DEVIL so that neither D is the firstletter nor L is the last letter is

(1) 36 (2) 114 (3) 42 (4) 78


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67. There are seven greeting cards, each of a different colour and seven envelopes of the sameseven colours. The number of ways in which the cards can be put in the envelopes so thatexactly four of the cards go into the envelopes of the right colours is

(1) 7 32 C (2)7

3C (3)4

33! C (4)7 4

3 33! C C

68. Number of ways in which 5 distinct balls can be put in to three identical boxes so that no boxis empty, is(1) 75 (2) 60 (3) 50 (4) 25

69. If a denotes the number of permutations ofx+ 2 things taken all at a time, b the number ofpermutations ofxthings taken 11 at a time and c the number of permutations ofx 11 things

taken all at a time such that 182 ,a bc then the value of x is(1) 15 (2) 12 (3) 10 (4) 18

70. In a chess tournament, where the participants were to play one game with another. Two chessplayer fell ill, having played 3 games each. If the total number of games played is 84, thenumber of participants at the beginning was(1) 15 (2) 16 (3) 20 (4) 21

71. The number of different combinations that can be formed out of the letters of the wordINFINITEtaken four at a time, is(1) 20 (2) 22 (3) 24 (4) 120

72. The coefficient of a10b7c3 in (bc+ ca+ ab)10is(1) 60 (2) 120 (3) 30 (4) 45

73. LetR= 2

2 3n

andf=R [R] where [.] denotes the G.I.F. ThenR(1 f) =

(1) 1 (2) 22n (3) 22n 1 (4) 2nCn


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74. If 62 2 12

1 2 121 2 1 ....... x x a x a x a x , then the expression a2+ a4+ a6+ ....a12has the value :(1) 32 (2) 63 (3) 64 (4) 31

75. In the expansion of

65611/3 1/9

7 11 the number of terms free from radicals is(1) 730 (2) 720 (3) 715 (4) 725

76. The value of0

n ji j n

i C is equal to

(1) 3( 1) 2 nn n (2) 2 32 nn (3) 3( 1) 2 nn n (4) None of these

77. The coefficient ofx53in the expansion of100

100 100

0

( 3) 2

m mmm

C x is

(1) 100 47C (2)100

53C (3)100

53C (4)100

100C

78. Find the equation of the circle having center at (2, 3) and which touchesx+y= 1(1) (x 2)2+ (y 3)2= 8 (2) (x 2)2+ (y+ 3)2= 8(3) (x+ 2)2+ (y+ 3)2= 8 (4) (x+ 2)2+ (y 3)2= 8

79. Find the image of the circlex2+y2 2x+ 4y 4 = 0 in the line 2x 3y+ 5 = 0(1) (x+ 3)2+ (y+ 4)2= 8 (2) (x 3)2+ (y 4)2= 9(3) (x+ 3)2+ (y 4)2= 9 (4) (x+ 3)2+ (y 4)2= 8

80. Find the greatest distance of the point P(10, 7) from the circlex2+y2 4x 2y 20 = 0.

(1) 10 (2) 15 (3) 5 (4) 20

81. Find the length of the intercept, the circlex2+y2+ 10x 6y+ 9 = 0 makes on thex-axis(1) 7 (2) 8 (3) 9 (4) 10


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82. Find the equation of the tangent to the circlex2+y2 6x+ 4y= 12 which is parallel to thestraight line 4x+ 3y+ 5 = 0(1) 4x+ 3y+ 19 = 0 (2) 4x+ 3y 19 = 0(3) 4x+ 3y+ 7 = 0 (4) 4x+ 3y+ 13 = 0

83. The line 2xy+ 1 = 0 is tangent to the circle at the point (2, 5) and the center of the circle lies

onx 2y= 4. The radius of the circle is

(1) 3 5 (2) 5 3 (3) 2 5 (4) 5 2

84. A straight lineLthrough the point (3, 2) is inclined at an algne 60 to the line 3 1.x y If

Lalso intersects thex-axis, then the equation ofLis

(1) 3 2 3 3 0y x (2) 3 2 3 3 0y x

(3) 3 3 2 3 0y x (4) 3 3 2 3 0y x

85. Consider the pointsA(0, 1) andB(2, 0), and Pbe a point on the line 4x+ 3y+ 9 = 0. Thecoordinates of Psuch that | PA PB| is maximum are

(1)12 17

,5 5

(2)84 13

,5 5

(3)6 17

,5 5

(4) (0, 3)

86. LineLhas intercepts aand bon the coordinate axes. When the axes are rotated through agiven angle keeping the origin fixed, the same lineLhas interceptspand q. Then

(1) a2+ b2=p2+ q2 (2) 2 2 2 21 1 1 1

a b p q

(3) a2+p2= b2+ q2 (4) 2 2 2 21 1 1 1a p b q


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87. The linex+ 3y 2 = 0 bisects the angle between a pair of straight lines of which one hasequationx 7y+ 5 = 0. The equation of the other line is(1) 3x+ 3y 1 = 0 (2) x 3y+ 2 = 0(3) 5x+ 5y 3 = 0 (4) x 3y 2 = 0

88. The image of P(a, b) on the liney= xis Qand the image of Qon the liney=xisR. Then themidpoint of PRis(1) (a+ b, b+ a) (2) ((a+ b)/2, (b+ 2)/2)(3) (a b, b a) (4) (0, 0)

89. If the equation of base of an equilateral triangle is 2xy= 1 and the vertex is (1, 2), then thelength of the sides of the triangle is

(1)20

3(2)

2

15(3)

8

15(4)

15

2

90. The number of values of afor which the lines2x+y 1 = 0, ax+ 3y 3 = 0, and 3x+ 2y 2 = 0 are concurrent is(1) 0 (2) 1 (3) 2 (4) infinite

iit jee mains question paper (10!04!2016) - xi

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