Max Marks:360

JEE-MAINIMPORTANT INSTRUCTIONS:

There are three parts in the question paper A, B, C consisting of Physics, Chemistry andMathematics having 30 questions in each part of equal weightage. Each question is allotted 4(four) marks for each correct response.Candidates will be awarded marks as stated above in instruction for correct response of eachquestion. 1/4 (one fourth) marks will be deducted for indicating incorrect response of eachquestion. No deduction from the total score will be made if no response is indicated for anitem in the answer sheet.There is only one correct response for each question. Filling up more than one response ineach question will be treated as wrong response and marks for wrong response will bededucted accordingly as per instruction

PHYSICS1. If 2 3 6a i j k

and 3 4b i j

then

Projection of on

Projection of on

a b

b a

1)7

52)

5

73)

4

94) None of these

2. A student is experimenting with resonance tube apparatus in physics lab to find thespeed of sound at room temperature. He got resonating lengths of air column as 17 cmand 51 cm, using tuning fork of frequency 512 Hz. Find the speed of sound at roomtemperature and specify , whether the side water reservoir was moved upward ordownward to obtain the second resonance (51cm) ?1) 348 m/s , downwards 2) 348 m/s , upwards3) 332 m/s , downwards 4) 332 m/s, upwards

3. A small body is released from rest on a smooth inclined plane at 0t . Velocity versustime graph of the body as shown in the figure. The angle of inclination of the planewith horizontal is 210g ms

/V m s

10

O 2 sect

1) 030 2) 045 3) 1 1tan

2

4) 1tan 5

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4. In a circular motion of a particle, the tangential acceleration of the particle is given by29 /ta m s . The radius of the circle is 4m. The particle was initially at rest. Time after

which total acceleration of the particle makes an angle of 045 with the radialacceleration is

1)1

sec3

2)2

sec3

3) 1sec 4)4

sec3

5. The potential energy in joule of a particle of mass 1 kg moving in x - y plane obeysthe law, 3 4x y . Here x and y are in meters. If the particle is at rest at (6m, 8m) attime 0, then the work done by conservative force on the particle from the initialposition to the instant when it crosses the x -axis is1) 25 J 2) 25 J 3) 50 J 4) 50 J

6. A particle of mass 0m , travelling at speed 0v , strikes a stationary particle of mass

02m . As a result, the particle of mass 0m is deflected through 045 and has a final

speed of 0

2

v. Then the speed of the particle of mass 02m after this collision is

1) 0

2

v2) 0

2 2

v3) 02v 4) 0

2

v

7. A thin hollow sphere of mass m is completely filled with non viscous liquid of massm . When the sphere roll-on horizontal ground such that centre moves with velocity v ,kinetic energy of the system is equal to

1) 2mv 2) 24

3mv 3) 24

5mv 4) None of these

8. Three identical particles each of mass M move along a common circular path of radiusR under the mutual interaction of each other. The velocity of each particle is

1)2

3

GM

R2)

3

GM

R3)

3

GM

R4)

2

3

GM

R9. Two simple harmonic motions are represented by the following equations

40siny t and 2 10 sin cosy t c t . If their displacement amplitudes are equal,

then the value of c (in appropriate units) is

1) 13 2) 15 3) 17 4) 410. A bob of mass 10 kg is attached to a wire 0.3 m long. Its breaking stress is

7 24.8 10 /N m . Then area of cross-section of the wire is 6 210 m . What is themaximum angular velocity with which it can be rotated in a horizontal circle ?1) 8 rad/s 2) 4 rad/s 3) 2 rad/s 4) 1 rad/s

11. A body of density is dropped from rest from a height h into a lake of density

. The maximum depth the body sinks inside the liquid is (neglect viscous

effect of liquid)

1)h

2)

h

3)h

4)h

12. A string of length ‘L’ is fixed at both ends. It is vibrating in its 3rd overtone with

maximum amplitude ‘a’. The amplitude at a distance3

Lfrom one end is

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1) a 2) 0 3)3

2a 4)

2

a

13. A source is moving with constant speed 20 /sv m s towards a stationary observer due

east of the source. Wind is blowing at the speed of 20 m/s at 060 north of east. Thesource has frequency 500 Hz. Speed of sound 300 /m s . The frequency registered bythe observer is approximately1) 541 Hz 2) 552 Hz 3) 534 Hz 4) 517 Hz

14. Switch S is closed at time 0t . Which one of the following statements is correct ?

.. ..

..

1E

R

S

2E

1r 2r

1) Current in the resistance R increases if 1 2 2 1E r E R r 2) Current in the resistance R increases if 1 2 2 1E r E R r 3) Current in the resistance R decreases if 1 2 2 1E r E R r 4) Current in the resistance R increases if 1 2 2 1E r E R r

15. A source of emf 10E V and having negligible internal resistance is connected to avariable resistance. The resistance varies as shown in figure. The total charge that haspassed through the resistor R during the interval from 1t to 2t is

40

20

1 10t s 2 30t s

R

t

1) 40log 4e 2) 30log 3e 3) 20log 2e 4) 10log 2e16. Six charges are placed at the vertices of a regular hexagon as shown in the figure. The

electric field on the line passing through point O and perpendicular to the plane of thefigure as a function of distance x from point O is x a

aQ Q

O

Q

Q Q

Q

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1) 0 2)3

0

Qa

x3)

30

2Qa

x4)

30

3Qa

x17. The figure shows a graph of the current in a discharging circuit of a capacitor through

a resistor of resistance 10

10

2.5

2 t s

i A

1) The initial potential difference across the capacitor is 100 V

2) The capacitance of the capacitor is1

10ln 2F

3) The total heat produced in the circuit will be500

ln 2J

4) All of the above18. A capacitor of capacitance C is charged to a potential difference V from a cell and

then disconnected from it. A charge Q is now given to its positive plate. Thepotential difference across the capacitor is now

1) V 2)Q

VC 3)

2

QV

C 4)

QV

C , if Q CV

19. Equal currents are flowing in three infinitely long wires along positive ,x y and z

directions. The magnetic field at a point 0,0, a would be ( i current in each wire)

1) 0

2

ij i

a

2) 0

2

ii j

a

3) 0

2

ii j

a

4) 0

2

ii j

a

20. A uniformly charged ring of radius R is rotated about its axis with constant linearspeed v of each of its particles. The ratio of electric field to magnetic field at a point Pon the axis of the ring at a distance x R from centre of ring is (c is speed of light)

x R

PO

v

1)2c

v2)

2v

c3)

v

c4)

c

v21. Two parallel long straight conductors lie on a smooth plane surface. Two other

parallel conductors rest on them at right angles so as to form a square of side a . Auniform magnetic filed B exists at right angles to the plane containing the conductors.Now conductors start moving outward with a constant velocity 0v at 0t . Then

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induced current in the loop at any time t is ( is resistance per unit length of theconductors)

B0v

1)

0

0

aBv

a v t 2) 0

2

aBv

3) 0Bv

4) 0

2

Bv

22. When an alternating voltage of 220 V is applied across a device P, a current of 0.25 A

flows through the circuit and it leads the applied voltage by an angle / 2 radian.When the same voltage source is connected across another device Q, the same currentis observed in the circuit but in phase with the applied voltage. What is the currentwhen the same source is connected across a series combination of P and Q ?

1)1

4 2A lagging in phase by / 4 with voltage

2)1

4 2A leading in phase by / 4 with voltage

3)1

2A leading in phase by / 4 with voltage

4)1

4 2A leading in phase by / 2 with voltage

23. Two identical glass3

2g

equi convex lenses of focal length f are kept in

contact. The space between the two lenses is filled with water4

3w

. The focal

length of the combination

1) f 2)2

f3)

4

3

f4)

3

4

f

24. A car is fitted with a convex mirror of focal length 20cm. A second car 2m broad and1.6m high is 6m away from the first car. The position of the second car as seen themirror of the first car is1) 19.35 cm 2) 17.45cm 3) 21.48 cm 4) 5.49 cm

25. Young’s double slit experiment is made in a liquid. The 10th bright fringe in liquid lieswhere 6th dark fringe lies in vaccum. The refractive index of the liquid isapproximately1) 1.8 2) 1.54 3) 1.67 4) 1.2

26. When a surface is illuminated with light of wavelength , the stopping potential is V.When the same surface is illuminated by light of wavelength 2 , the stopping

potential is3

V. Threshold wavelength for the metallic surface is

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1)4

3

2) 4 3) 6 4)

8

3

27. A stationary hydrogen atom of mass M emits a photon corresponding to the first lineof Lyman series. It ‘R’ is the Rydberg’s constant, the velocity that the atom acquires is

1)3

4

Rh

M2)

4

Rh

M3)

2

Rh

M4)

Rh

M

28. When a block of iron floats in mercury at 00 C , a fraction 1K of its volume is

submerged, while at the temperature of 060 C a fraction 2K is seen to be submerged. Ifthe coefficient of volume expansion of iron is

Fe and that of mercury is

Hg , then

the ratio 1

2

K

Kcan be

1)1 60

1 60Fe

Hg

2)

1 60

1 60Fe

Hg

3)

1 60

1 60Fe

Hg

4)

1 60

1 60Fe

Hg

29. One mole of a monoatomic ideal gas undergoes the process A B in the given P- Vdiagram. The specific heat for this process is

06P

03P

0V 05V V

P

A

B

1)6

R2)

11

6

R3)

13

6

R4)

12

R

30. A long horizontal gas filled tube of length 2L closed at both ends is rotated about avertical axis through its centre normal to its length with an angular velocity . If 0P

is the pressure at the centre, T is temperature in Kelvin scale, R is gas constant per unitmass, the pressure P at the end B will be

2L

A B

1)2 2

0P LP

T

2)

2 2

20

L

RTP P e

3) 0P L

PRT

4) 0

L

RTP P e

CHEMISTRY

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31. Which of the following compounds show geometrical isomerismi) 3 4 2[ ( ) ]Co NH Cl ii) 2 2[ ( ) ]Co en Cl iii) 2[ ( ) ]Pt gly iv) 3

3[ ( ) ]Co en

1) i,ii and iii 2) ii, iii and iv 3) i, iii and iv 4) i, ii,iii and iv32. 25ml of 2 2H O on treatment with excess of acidified KI solution liberates iodine.

Liberated iodine requires 40ml of 0.4N 2 2 3Na S O solution. The volume strength of

2 2H O solution is

1) 1.344 2) 3.584 3) 0.64 4) 1.58433. The osmotic pressure of 0.1M solution of 2MgCl at 300K is 4.92atm. The percentage

ionization of the salt is1) 20% 2)39% 3)49% 4)69%

34. The Gibb’s Energy for the decomposition of 2 3Al O at 5000C is as follows

2 3 22 4

; 965 /3 3 rAl O Al O G KJ mole

The potential difference needed for electrolytic reduction of 2 3Al O at 5000C is at least1) 2.5V 2) 3V 3) 4.5V 4) 5.0V

35. An impure sample of NaCl weighing 2 grams was dissolved in water and excess of

3AgNO solution was added. The weight of precipitate formed was 0.287g. The

percentage purity of the sample is1) 11.7% 2) 5.85% 3) 25% 4) 2.85%

36. The density of an ionic crystal is 32.75g cm and edge length of unit cell is 660 pm.The formula weight of ionic compound is 119. The number of unit cells present in23.8 g of the ionic compound is1) 231.2046 10 2) 223.011 10 3) 226.023 10 4) 221.2046 10

37. An organic compound has 14% of nitrogen. It is subjected to kjeldahl’s method andthe ammonia evolved is absorbed in 100ml of normal sulphuric acid. About 400ml of

water was added. And 20 ml of this new solution now required 16ml5

NNaOH for

complete neutralization. Calculate the original weight of the organic compound taken.1) 20 gm 2) 1.4 gm 3) 4 gm 4) 2 gm

38. The number of monochloro derivatives that the compound ‘D’ can give, ,

33H O H Ca drydistillation Zn Hg HClCH CN A B C D

1) 3 2) 4 3) 2 4) 1

39. If H, D, He atoms are travelling with same velocity, the ratio of their deBrogliewavelength is1) 1: 1: 1 2) 1: 2: 4 3) 2: 1: 4 4) 4: 2: 1

40. For the decomposition of 5PCl g in a closed vessel, the degree of dissociation is ‘x’at a total pressure ‘P’.

5 3 2 ;PCl g PCl g Cl g Kp

Which among the following relations is correct?

1) p

p

Kx

K P

2) p

p

K Px

K

3) px K P 4) 1

px

K P

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41. Observe the following statementsa) The almost identical radii of Zr and Hf is consequence of Lanthanide contractionb) 2Eu act as a strong reducing agentc) An alloy of lanthanoid metal called misch metal is used in making bulletsd) Actinoid contraction is greater from element to element than lanthanide contraction.The correct statements are1) a, b, c 2) a, b, c, d 3) b, c, d 4) a, c, d

42. 22O ZnOre CN H O X Y metal . X and Y in this reaction is

1) 2

2 4;X Ag CN Y Zn CN

2) 2

4 4

2;X Ag CN Y Zn CN

3) 2

2 4;X Au CN Y Zn CN

4) 1 and 3

43. In which of the following pair of compounds, the first compound have moredipolemoment than the second one.1) 3 3,NF NH 2) m-dichloro benzene, o- dichloro benzene3) 2 2,H S H O 4) 3 3,CH Cl CHCl

44. The pH of a sample of KOH solution is 12.6990. The weight of solute required toprepare 5 lit of the solution is1) 14g 2) 56g 3) 28g 4) 11.2g

45. Which of the following fibre is of polyamides?1) Dacron 2) Orlon 3)Nylon 4) Rayon

46. Which among the following are correct statementsa) Order of O O bond length is 2 2 26O AsF O KO b) Though Ethylalcohol and Dimethyl ether have same molecular weights, Dimethylether is more volatile than Ethylalcohol.c) The order of bond order is 2 2 2

2N N N

d) Ice has more density than water1) a, b, d 2) a, b, c 3) a, c, d 4) a, b, c, d

47. The correct order of coagulation power of different ions is

1) 23Al Ba Na

2) 24

434 6Cl SO PO Fe CN

3) 24

4 346Fe CN PO SO Cl

4) 3 2Al Ba Na

48. A salt ‘X’ on heating liberate one coloured gas and another coloureless gas. Both thegases are paramagnetic. The salt ‘X’may be1) 3NaNO 2) 3KNO 3) 2 3Na CO 4) 3LiNO

49. Compressibility factor for 2H behaving as real gas is

1) 1 2) 1a

RTV

3) 1Pb

RT

4) 1

RTV

a

50. In which of the following arrangements the order is not according to the propertyindicated against it ?

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1) 2 2 3O F Na Mg Al (ionic radii)2) F Cl Br I (Electron gain enthalpy)3) B C O N (First ionization enthalpy)4) 5 72 2 3 2SiO P O SO Cl O (acidic nature)

51. The composition of a sample of Ion oxide is 0.93 1.0Fe O . The percentage of iron present

in the form of 3Fe is1) 85% 2)15% 3) 12% 4) 76%

52. 93.75% of a I order reaction is completed in 120 minutes. If initial concentration of thereactant is 2 mole/lit, the rate of reaction at the end of 120 min is1) 2 14.62 10 minM 2) 3 12.31 10 minM

3) 3 12.88 10 minM 4) 4 16.93 10 minM 53. Which of the following is wrong statement.

1) 2 5I O is a very good oxidizing agent and is used in the estimation of carbon

monoxide.2) 2ClO is used as bleaching agent for paper pulp and textiles.

3) When HCl reacts with finely powdered iron, it forms ferrous chloride and not ferricchloride.4) The inter halogen compound 1XX hydrolysis as follows.

1 12XX H O HX HOX [when X = larger halogen]

54. Which of the following is wrong1) 3 3H BO is monobasic and Lewis acid2) 3 3H BO is tribasic and Lewis acid3) In solid state of orthobenzoic acid, 3( )B OH units are hydrogen bonded together intotwo dimentional sheets.4) Aqueous solution of Borax acts as a Buffer solution.

55. An organic compound (A ) with molecular formula 8 8C H O forms an orange-redprecipitate with 2,4 DNP and gives yellow precipitate on heating with iodine inpresence of NaOH . It neither reduces tollen’s or Fehling’s reagent nor does itdecolourise bromine water or Bayer’s reagent. On drastic oxidation with chromic acidit gives carboxylic acid having molecular formula 7 6 2C H O . Then A and B are1) 6 5 3 6 5 3,C H COCH C H COOCH

2) 6 5 2 6 5,C H CH CHO C H COOH

3) 6 5 2 6 4 2,C H CH CHO C H CH OH

4) 6 5 3 6 5,C H COCH C H COOH

56. An aldehyde, (P) which does not undergo self aldol condensation gives benzaldehydeand two moles of (Q) on ozonolysis. Compound ( Q), on oxidation with silver ionsgives oxalic acid. The structure of ( P) is given as

1)

2CH CH CH CH CH CHO

2)

CH CH CH CH CHO

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3)

C C CHO

4)CH CH C CHO

O

57. The product of the following I and II sequence are related as

CH3 C C CH3

(i) H2/Pd/CaCO3 (ii) Br2/CCl4

(i) Br2(1 eq.)/ CCl4 (ii) H2 / Pd

?

?

(I)

(II)

1) Diastereomers 2)Identical3) Enantiomers 4) Geometrical isomers

58. Which of the following sequence of reagent is the good means to furnish theconversion ?

2 2 2R CH OH R CH NH

(a) 4 2 3, , , ,KMnO SOCl NH NaOBr

(b) 2 2, , /SOCl NaCN H Ni

(c) 3CrO in dilute acetone, 3 2, ,NH H Ni

(d) 03 4,300 , ,Cu C NH LiAlH

1) a, b, c, d 2) a, b, c 3) b, c, d 4) c, d59. Consider the following statements:

a) Keratin & Myosin are fibrous proteinsb) Deficiency of vitamin C causes disease bleeding gums (scurvy)c) D-glucose and D- mannose are C-2 epimers.d) Fructose does not reduse fehling solutionWhich of the given statements are correct1) a, c. d 2) a, b, d 3) a, b, c 4) a, b, c, d

60. The correct order of stability of following carbanions

3 6 5 2 3 3 3. . . .I CH II C H CH III CCl IV CH C

1) II > I > III > IV 2) II > III > I > IV3) III > II > IV > I 4) III > II > I > IV

MATHEMATICS61. Let S be the set of real numbers. For a , b S , relation R is defined by

a R b a b 1 then R is

1) only reflexive 2) only symmetric3) only transitive 4) Reflexive & symmetric

62. Given that matrix3 2

1 4

2 2

x

A y

z

. If 2013xyz and 8 4 3 2012x y z then A adj A is

equal to

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1)68 0 0

0 68 0

0 0 68

2)34 0 0

0 34 0

0 0 34

3)29 0 0

0 29 0

0 0 29

4)58 0 0

0 58 0

0 0 58

63. In a PQR , if 3sin 4 cos 6P Q and 4sin 3cos 1Q P then angle ‘R’ is

1)6

2)4

3) 3

4

4) 5

6

64. 0,2 and 1 2 3, ,z z z are three complex numbers such that they are collinear and

1 2 31 sin cos 1 2z z z =0 .If at least one of the complex numbers 1 2 3, ,z z z

is non- zero then number of possible values of is1) Infinite 2) 0 3) 2 4) 4

65. The number of real negative terms in the binomial expansion of

4 21 , , 0nix n N x is

1) n 2) n +1 3) 1n 4) 2n

66. Let 2 , 4 133nf x x Rand n N f and 5 255f then sum of the

factors of 3 2f f is

1) 20 2) 60 3) 21 4) 5967. In a sequence of 21 terms the first 11 terms are in A.P. with common difference 2 and

the last 11 terms are in G.P. with common ratio 2. If the middle term of the A.P. isequal to the middle term of the G.P., then the middle term of the entire sequence is

1)10

31

2)

630

31

3)

32

31

4)

320

31

68. Value of34

4xsin x dx

where [ ] denotes step function is

1) 0 2)5

4

3)

7

4

4)

3

4

69. If

, ,2 2

f x f yx yf x y R

and ' 0 1, 0 1f f then 2f

1) 1

22) 1

2 3) 1 4) -1

70. The equation of the plane containing the line 1

2

x = 1

1

y

= 3

4

z and perpendicular

to the plane 2 12x y z is1) 9 2 5 4 0x y z 2) 9 2 5 4 0x y z 3) 9 2 5 4 0x y z 4) 9 2 5 4 0x y z

71. If the lines x = k : k = 1, 2, 3 ……., n meet the line y = 3x + 4 at the points

, : 1,2,3........k k kA x y k , n then the ordinate of the center of mean position of the

points , 1,2,3...kA k , n is

1) 1

2

n 2) 3 11

2

n 3) 3 1

2

n 4) 11

2

n

72. The chords of contact of the pair of tangents to the circle 2 2 1x y drawn from anypoint on the line 2 4x y pass through the point

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1)1 1

,2 4

2)1 1

,4 2

3)1

1,2

4)1

,12

73. Total number of points of discontinuity of ( ) [4 3sin ] (0, )f x x in { [.] denotesgreatest integer function. }1) 2 2) 3 3) 5 4) 6

74. ‘A’ is a square matrix, if all elements in nA become zero, as n , we saylim nA On now 0 ,

x xA x

x x

then the value of ‘x’, such that lim nn A O is

1)2

10 x 2)

4

30 x 3) 10 x 4) x > 1

75. Maximum number of common normals of y2 = 4x and x2 = 4y that can be drawn isequal to1) 1 2) 3 3) 5 4) 6

76. A variable triangle ABC is inscribed in a circle of diameter x units. At a particularinstant the rate of change of side ‘a’ is / 2x times the rate of change of the oppositeangle A then A =1) / 6 2) / 3 3) / 4 4) / 2

77. The line 3 2 24x y meets x-axis at A and y-axis at B. The perpendicular bisector ofAB meets the line passing through (0, -1) and parallel to x-axis at ‘C’. Then the areaof ABC is (in square units)1) 83 2) 87 3) 90 4) 91

78. The area bounded by x

y xe and the lines x = 1, y = 0 is ( in sq.units)

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

79. The solution of the differential equation2

22

3 xd ySin x e x

dx when 1 0 1y and

y(0) = 0 is

1)4 3 1

19 12 3

Sin x xe xx 2)

4 3 1

9 12 3

Sin x xe xx

3)4Cos 3 1

19 12 3

x xe xx 4)

4Cos 31

9 12 3

x x xex

80. A particle acted by constant forces 4 3i j k $ $ $ and 3i j k $ $ $ is displaced from the

point 2 3i j k $ $ $ to the point 5 4 .i j k $ $ $ The total work done by the forces is1) 30 units 2) 40 units 3) 50 units 4) 20 units

81. A point (a,b) is called a good point if both ‘a’ and ‘b’ are integers. The number ofgood points on the curve xy= 225 are1) 9 2) 10 3) 16 4) 18

82. The point ‘B’ is the image of ‘A’ in the line 4 0x y and ‘C’ is the image of ‘B’ inthe line 2 7 0x y , if 1,6A then the circumcentre of the triangle ABC is

1)11 1

,3 3

2)11 1

,3 3

3)11 1

,3 3

4)11 1

,3 3

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83. If n N & n > 1 then the digit in unit’s place of the number100 n2

k 0

k 2

1) 0 2) 6 3) 2 4) 484. The number of non zero solutions of the system of equations

2 2 2

2 2 22 2 2

, ,1 1 1

z x yx y z

z x y

is

1) 0 2) 1 3) 2 4) infinite85. The probability that 1 1sin sin cos cosx y is an integer when , 1,2,3,4x y is

1) 1

162) 3

163) 15

16d) 5

1686. The area bounded by the circles x2 + y2 = 1 & x2 + y2 = 4 and the pair of lines

2x2 – 3xy – 2y2 = 0 (y>0) is ___( in sq.units)1) /4 2) /2 3) 3 /4 4) /3

87. A random variable X has its range {0, 1, 2} and P(X = 0)=3c3, P(X = 1) = 4c – 10c2,P(X=2)=5c–1 then P 0 X 3 ____

1) 1

32) 8

93) 7

84) 1

988. A tower ABCD stands on a level ground with foot A. At a point P on the ground, the

portion AB, AC and AD subtends angles , and respectively. If

AB a, AC b, AD c , AP x and 0180 then 2a b c x =

1) abc 2) 1

abc3) a + b – c 4) a – b – c

89. 1tan 3x n is a solution of the equation10

12 tan 2 1 0cos

xx

for

1) no value of n 2) all integral values of n3) even values of n 4) odd values of n

90. Suppose a population ‘A’ has observations 101,102,......200 and another population ‘B’has observations 151,152,.......250 . If AV and BV represent variances of two populations

respectively then A

B

V

V

1)9

42)

4

93)

2

34) 1

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