Iit jee Model Paper 4

8/20/2019 Iit jee Model Paper 4

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JEE-MAIN_2013 MODEL

1. The test is of 3 hours duration.

2. The Test Booklet consists of 90 questions. The maximum marks are 360.3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry

and Maths having 30 questions in each part of equal weightage. Each question is

allotted 4 (four) marks for correct response.

4. Candidates will be awarded marks as stated above in instruction No. 4 for correct

response of each question. (1/4) (one fourth) marks will be deducted for indicating

incorrect response of each question. No deduction from the total score will be

made if no response is indicated for an item in the answer sheet.

5. There is only one correct response for each question. Filling up more than one

response in any question

will be treated as wrong response and marks for wrong response will be deducted

accordingly as per instructions 5 above

PHYSICS1. In an experiment to measure the length of a rod by four different instruments, the

measurement are reported asA)200.0 cm B)20 cm C)20.00 cm D)0.2000 cm

From the above data, we can infer that

A) All measurements have same accuracy B) A has least accuracy

C) B has least accuracy D) D has least accuracy

2. Which of the following plots correctly represents variation of the magnitude of radial

acceleration | | Ra with time t for a particle projected at t = 0 with speed 0v at an angle

θ above the horizontal?

A) B)

C) D)

3. In the given figure, a smooth parabolic wire track lies in the vertical plane(x-y plane).

The shape of track is defined by the equation (where a is constant). A ring of mass m

which can slide freely on the wire track, is placed at the position A(a, a). The track is


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C) 1 2 33

mgT T T D) 1 1 2 2 3 3T T T l l l

8. A block of mass 2 kg is to be lifted with constant velocity by applying force F down

the rope that passes over a pulley having coefficient of friction µ . The pull required is

A) 22geπµ

B) 2g C) 2geπµ D) 42geπµ

9. A chain of mass per unit length λ and length 1.5 m rests on a fixed smooth sphere of

radius 2 R π m such that A end of chain is at the top of sphere while the other end is

hanging freely. Chain is held stationary by a horizontal thread PA. The tension in the

thread is

A)1 2

2gλ

π

B)

2

2g

πλ

π

C)

2gλ

π

D) None of these

10. Figure shows a disc of mass M and radius R hinged at the centre. A small ball of mass

2

M is attached to point P with a thread of length 2R and held at rest at position shown.

Now, the balls is released to fall under gravity with what angular speed the disc starts

turning when the string becomes taut?

A)

2

g

R

B) g

R

C) R

g

D)2g

R11. A particle is projected from ground with speed u such that the horizontal range is R

and maximum height is H. The angular velocity of the particle about the point of projection, when it is at the highest point of its trajectory is


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A) 2 2 2 24 16

HRu

R H R H B)

2 2 2 24

4 16

HRu

R H R H

C) 2 2 2 2

8

4 16

HRu

R H H R D)

2 216

uR

H R H

12. Two identical discs of mass M and radius R are in contact with each other on smooth

horizontal surface. The disc A is fixed while B start rolling on circular path such thatthere is no slipping. The disc B makes one revolution around A in T time. Calculate

kinetic energy of the disc B.

A)2 2

2

16 M R

T

π B)2 2

2

3 MR

T

π C)2 2

2

24 MR

T

π D)2 2

2

12 MR

T

π

13. In the case of geostationary satellite, the

A) Rotation of the earth and the revolution of the satellite need not to be about

common axis

B) Rotation of the earth and revolution of the satellite will be in opposite directionsC) Angular velocity of the earth’s rotation and angular velocity of revolution of the

satellite will be equal and be in the same directionD) Angular velocity of the earth’s rotation and angular velocity of revolution of the

satellite will not be equal14. A rectangular container of base dimensions 2 1m m and height 0.5 m is filled with

water upto height of 0.2m. The mass of the empty container is 1 kg. The coefficient of

friction between container and plane is 0.5. The container is placed on the plane

inclined at 450

to the horizontal. The angle of the water surface to the horizontal is

A) 11

tan2

B) 1tan 2 C) 11

tan3

D) 1tan 3

15. The frequency of first overtone of a closed organ pipe of length L is f 1. A hole is made

at a distance

6

Lfrom the closed end. Now the frequency of first overtone of open pipe

is f 2. Then1

2

f

f is

A)4

5B)

5

4C)

8

5D)

5

8

16. One end of a string of length L is tied to ceiling of lift accelerating upwards with an

acceleration 3g. The other end of the string is free. The linear mass density of string

varies linearly from 0 to λ from bottom to top. Then correct statement for wave

travelling in string

A) Wave speed is increasing as it travels from bottom to top

B) Acceleration of wave on string is uniform

C) Time taken by pulse to reach from bottom to top will be2 L

g


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D) All of these

17. Statement-I: A planet may orbit around a star either in orbit P or orbit Q. The speed

of a planet at O is same for both orbits. AndStatement-II: The radius vector of point O from the sun is same for both orbit

P and Q.

[Note: Centre of circle consider with focus of the ellipse]

A) Statement-1 is True, Statement-2 is True; Statement -2 is a correct explanation for

Statement-1.

B) Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct

explanation for Statement-1.C) Statement -1 is True, Statement-2 is False.

D) Statement -1 is False, Statement-2 is True.18. P-V diagram of ideal gas is as shown in figure. Work done by the gas in the process

ABC is

A) 0 02PV B) 0 04PV C) 0 0PV D) 0 03PV

19. One mole of ideal gas whose adiabatic exponent4

3γ undergoes process

1200P

V

then change in internal energy of gas when volume changes from 32m to 34m is

A) 400 J B) 800 J C) 1200 J D) None of these

20. A capacitor is initially connected to a battery of EMF 3 V after a long time. At t = 0,

switch is thrown to B state. Now charge on capacitor at any instant is given by

A) / 2 t RC q C V V e B) / 2 t RC q C V V e

C) /2

2

t RC

q C V V e

D)

2 /

2

t RC

q C V V e

21. Consider the diagrams shown. Work done in transferring wire from position(1) to

position (2) is W1. Work done in transferring the wire from position (3) to position (4)

is W2 then


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A) 1

2

1W W

B) 2

1

1W W

C) 1 2 0W W D) 1W is positive, 2W is zero

22. A particle of mass m and charge q enters a region of magnetic field (as shown) with

speed v. There is a region in which the magnetic field is absent, as shown. The particleafter entering the region collides elastically with a rigid wall. Time after which the

velocity of particle becomes anti parallel to its initial velocity is

A) 42

m

qBπ B) 2

m

qBπ C) 2

4

m

qBπ D) 2 3

4

m

qBπ

23. Consider a wire of non-uniform cross-section. If the area of cross-section at point A is

double of the area of cross-section at point B. What is ratio of heat energy dissipated

in a unit volume at points A and B?

A)

1

2B)

2

1C)

1

4D)

4

1

24. Image in convex mirror, of the image of rod PQ in the plane mirror, is(radius of

curvature of mirror is 60 cm).

A) Virtual, erect and 6 cm long B) Real, inverted and 3 cm long

C) Virtual, erect and 3 cm long D) Real, inverted and 6 cm long

25. White light is used for double slit interference, for how many wavelengths, we get

maximum at point P shown here on the screen?


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A) 1 B) 2 C) 3 D) 726. When a monochromatic point source of light is at distance of 0.2 m from aphotoelectric cell, the cut off voltage and saturation current are respectively 0.6 V and

18 mA. If same source is placed 0.6 m away from photoelectric cell then

A) Stopping potential will be 0.2 volt B) Stopping potential will be 0.6 volt

C) Saturation current will be 6 mA D) Saturation current will be 4 Ma

27. The dependence of nuclear force on distance between nucleons is not known precisely,

but approximate variation is shown graphically. From graph which of following

statements cannot be concluded?

A) Nuclear force is repulsive for separation less than 0.5 fermi

B) Nuclear force is attractive for separation less than 0.5 fermi

C) Nuclear force is attractive for separation more than 0.5 fermi

D) Nuclear force is negligible when separation between nucleon is more than 10 fermi28. A point source of light is placed directly above an opaque sphere of radius y placed on

a horizontal surface

A) For2

3

y x , radius of shadow formed on horizontal surface is 2y

B) For x y , radius of the shadow formed on horizontal surface is 3 y

C) For2

3

y x and for surrounding medium having refractive index 3 , radius of

shadow formed on horizontal surface is 2y

D) For x = y and for surrounding medium having refractive index 3 , radius of the

shadow formed on horizontal surface is 2 y

29. Consider a hypothetical atom with single electron. In this atom, when an electron de-excites from energy level n x to 2n , wavelength λ of the radiation emitted is

given by2

24

Ax

xλ

(where A is a constant). Choose the correct alternatives.


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A) Least energetic photon emitted during such a transition will have wavelength 1.8 A

B) Most energetic photon emitted in such a transition will have wavelength A

C) Ionization potential of the atom in its ground state is1.8

hc

eA

D) Ionization potential of the atom in its first excited state is hc

eA

30. Choose the correct alternative.A) K α wavelength emitted by an atom of atomic number Z = 21 is λ , then

K α wavelength emitted by an atom of atomic number Z = 31 is4

9

λ

B) Half life of a radioactive substance is 5 years. Probability that a nucleus decays in

10 years is3

4

C) Mass number of a nucleus is always greater than its atomic number

D) Gamma rays are emitted due to nuclear de-excitation

CHEMISTRY31. Among the following hydroxides the one with lowest value of Ksp at ordinary

temperature.

A) 2

Ba OH B) 2

Mg OH C) 2

Ca OH D) 2

Be OH

32. Which of the following pairs can be distinguished by action of heat

1) 2 3 3 Na CO and CaCO 2) 2 2 2 2.6 .6 MgCl H O and CaCl H O 3) 3 32Ca NO and NaNO

A) 1 and 2 B) 1,2 and 3 C) 1 and 3 D) 1 only

33. 0200

2 6 3.2 C

g B H NH X Y

Number of double bonds in X.A) 3 B) 2 C) 4 D) 1

34.0200

3 4

C H PO X Y . The hybridization of ‘P’in X and Y.

A) 2 2sp and sp B) 3sp and sp C) 2sp and sp D) 3sp and no hybridization

35. H2SO4 is used to dry which of the following gases?

A) H2S B) CO2 C) NH3 D) all of these

36. Lowest boiling point is associated withA) HF B) HCl C) HBr D) HI

37. 2 2 2 23 2SiO H F X H O . During the formation of ‘X’ an intermediate product ‘Y’ is

formed. Hybridization of central atom in X and Y respectively

A) 3 2 2,sp d sp B) 3 3,sp d sp C) 3 2 3,sp d sp D) 3 3 2,sp d sp d

38. The percentage by volume of C3H8 in a mixture of C3H8, CH4 and CO is 36.5.

Calculate the volume of CO2 produced when 100 ml of the mixture is burnt in excessof O2A) 173 mL B) 253 mL C) 168 mL D) 223 mL

39. A complex is prepared by mixing CoCl3 and NH3. 0.1M solution of the complex was

found to freeze at 00.372 C . The formula of the complex is (molal depression constant

of water = 1.86 0 / C m )

A) 3 36Co NH Cl B) 3 25Co NH Cl Cl C) 3 24Co NH Cl Cl D) 3 33Co NH Cl

40. Magnetic moment of 3

6Cr CN

ion if it is a inner orbital complex.

A) 5.92 B.M B) 1.73 B.M C) 2.828 B.M D) 3.9 B.M


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41.

3CH

OH O

H

X

The product ‘X’ is

A)

3CH

OH O B)

3CH

OH HO

C)

3CH

O D)

3CH

O

42.

N

O

2 Br

Fe The Major Product formed is

A)

N

O

Br

B)

N

O

Br

C)

N

O

Br D)

N

OBr

43.

3CH

HOBr ' ' X

. No. of atoms undergoing tetrahedral hybridization in X.

A) 7 B) 6 C) 8 D) 9

44. 2

3

Hg

H Ph C C CH A

. (A) is

A)

Ph

O

3 H C B)

Ph

O

3 H C

C)

Ph

3 H C

OH

D)

Ph

3 H C

OH


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45. Which of the following readily undergo SN1

mechanism

A) 3CH Br B)

Br

C)

3CH

Br

D)

2 2CH CH Br

46. The appropriate reagent for the following transformation

3CH

O

HO HO

A) / Zn Hg HCl B) 2 2 / NH NH OH

C) 2 / H Ni D) 2 4 / / H Pd BaSO Quinoline

47. What is the shortest wavelength line in the Paschen series of 2 Li ion ?

A) 9

RB)

9

RC)

1

RD)

9

4

R

48. A certain hydrate has the formula 4 2. MgSO xH O .A quantity of 54.2 g of the compound

is heated in an oven to drive off the water .If the steam generated exerts a pressure of

24.8 atm in a 2.0 L container at 0120 C , calculate x.

A) 2 B) 5 C) 6 D) 7

49. Poly caprolactum is

A) Nylon 6,6 B) Perlon-L C) Dacron D)Glyptal50. Calculate 0 f H for 4UBr from the

0G of reaction and the 0S values of U (s),

( )2 4( ) Br l and UBr s are 50.3,152.3,242.6 (J / K – mol) respectively

0 12 42 ; 788.6 ;U S Br l UBr s G kJ mole

A) -822.1 kJ/mol B) -841.2 kJ/mol C) -775.6 kJ/mol D) -804.3 kJ/mol51. The equilibrium constant Kc for the reaction

4 22P g P gƒ

Is 1.4 at 4000C. Suppose that 3 moles of 4P g and 2 moles of 2P g are mixed in 2 litre

container at 0400 C . What is the value of reaction quotient (Q)?

A)3

2B)

2

3C) 1 D) 4/3

52. 20

amino group is present in

A) Tyrosine B) Lysine C) Proline D) Serine53. In the following reaction A B C , rate constant is 0.001 1 Ms . If we start with 1 M

of A then conc.of A and B after 10 minutes are respectively:

A) 0.5 M , 0.5 M B) 0.6 M , 0.4 M

C) 0.4 M , 0.6 M D) 0.2M, 0.8 M

54. The radioactive decay211 207

83 81 Bi Tl , takes place in 100 L closed vessel at0

27 C .Starting with 2 moles of 21183 1/ 2 130sec Bi t , the pressure development in the vessel

after 520 sec will be :

A) 1.875 atm B) 0.2155 atm C) 0.4618 atm D) 4.618 atm


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55. a pK of 4 NH is 9.26. Hence, effective range for 4 4 NH OH NH Cl buffer is about pH :

A) 8.26 to 10.26 B) 4.74 to 5.74

C) 3.74 to 5.74 D) 8.26 to 9.26

56. Which of the following is most soluble in water ?

A) 393 4 2 6 10sp Ba PO K B) 167 10sp ZnS K

C) 38

3 6 10spFe OH K

D)

18

3 4 1.8 10sp Ag PO K

57. A 100.0 mL dilute solution of Ag is electrolyzed for 15.0 minutes with a current of

1.25 mA and the silver is removed completely. What was the initial Ag ?

A) 12.32 10 B) 42.32 10 C) 32.32 10 D) 41.16 10

58. The Nernst equation 0 / ln E E RT nF Q indicates that the Q will be equal to

equilibrium constant cK when

A) 0 E E B) / 1 RT nF C) E = zero D) 0 1 E

59. Which of the following expressions is correct in case of a CsCl unit cell

(edge length, a)?

A) c ar r a B) / 2c ar r a C) 3 / 2c ar r a D) / 2c ar r a

60. On adding 3 AgNO solution into KI solution , a negatively charged colloidal sol is

obtained when they are in :

A) 50 ml of 0.1 M 3 AgNO + 50 ml of 0.1 M KI

B) 50 ML of 0.1 M 3 AgNO + 50 ml of 0.2 M KI

C) 50 ML of 0.2 M 3 AgNO + 50 ml of 0.1 M KI

D) 50 ML of 0.2M 3 25 mL 0.4 M KI AgNO

MATHEMATICS

61. If 2 y f x ax bx c ,where a, b and c are real numbers such that 2 4 0b ac ,then

A) 0ac x R

B) 0,af x x R

C) The shortest distance from the curve y= f x to the x -axis is2

4

4

b acd

a

D) All of the above

62. If I is the incentre of ABC with inradius r, circum radius R, then ( AI )( BI )(CI ) is

equal to

A) 22r R B) 24r R C) 38r D) 32 R

63. The number of roots of the equation 7

1

sin 7k

kx

sin 4 x in the interval 0,2π is

A) 3 B) 5 C) 7 D) 9

64. The fractional part of x ,

where 6 6 6 6

3 2 1 3 2 1 3 2 1 3 2 1 x

A) 0 B) 3 2 C) 3 2 3 D) 1 2 3

65. If

x = fractional part of x , then

12

sin 2 1lim x

x

x x

is equal to

A) 0 B) 1

C) does not exists D) 9


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66. Consider y f x such that 3 1 7 111 1 3 5 7 f x x x x x , then

A) 1,5 x are the local minima of y f x

B) 1,5 x are the local maxima of y f x

C) 3,7 x are not the local minima of y= f x

D) 3,7 x are the local maxima of y= f x

67. If

2 2

cos sin

2 sin cos sin cos

x x dx

x x x

=

1

1tan log

1

f x A f x B C

f x

, then

A) A= 3B B) sin cos

13

x x f x

C) 2 29 1 A B D) A= -2B68. Statement – I The value of the integral

/3

/ 6 1 tan

dx

x

π

π is equal to / 6π

Statement – II b b

a a f x dx f a b x dx

A) Statement I is true; Statement II is true ; Statement II is a correct explanation for

Statement I.B) Statement I is true; Statement II is true ; Statement II is not a correct explanation

for Statement I.

C) Statement I is true; Statement II is false

D) Statement I is false ; Statement II is true.

69. The number of roots of the equation 1 1 3sin sin 1

2

x x π is equal to

A) 0 B) 1 C) 2 D) 6

70. The number of solutions of sin cos tanθ θ θ in 0,π is

A) 0 B) 1 C) 2 D) 4

71. Area of the quadrilateral formed from tangents and normals drawn on the extremities

of the latusrectum of the parabola 2 4 y ax is

A) 2a B) 22a C) 24a D) 28a

72. The shortest distance between the line y x and the hyperbola2 2

19 4

x y is

A) 32

B) 23

C) 52

D) 9

73. The area of the parallelogram formed by the lines 1 x y

a b and the directrices of the

ellipse2 2

2 21

x y

a b with eccentricity , e and a, b being positive is

A)2

ab

eB)

2

4ab

eC)

2

2ab

eD)

2

9ab

e

74. One of the tangents drawn from the origin to the circle 2 2

6 6 18 x y are

A) 2 3 y x B) 2 3 y x C) y x D) y x 75. If 1 2,h h and 3 0h are in HP and


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1 2 2 3 3 1

2 3 3 1 1 2

3 1 1 2 2 3

h h h h h h

h h h h h h

h h h h h h

, then

A) is always positive B) is always negative

C) is positive, if 2h is negative D) is negative, if 3h is positive

76. There are 5 men and 5 women in a party. In how many ways can 5 dancing pairs be

selected ? ( each dancing pair consists of 1 man and 1 woman)A) 120 B) 44 C) 32 D) 10

77. In a party, there are 6 husband – wife pairs .Dance couples are formed randomly

choosing one man and one woman. The probability that H j

dances with7

W i, given

that H i

dances with , 1, 2, 3, 4, 5, 6W i j i j

A)265

720B)

1

265C)

10

265D)

263

500

78.

3

1/ 3

log x

x dx is equal toA) 0 B) log 3 C) 2 log 3 D) 1

79. Let / 2 / 2, 1a e e b eπ π π and /42c eπ , then

A) ac C) ab

80. The order and degree of the differential equation

1/3 2/3 13 2

3 20

d y d y dy

dx dx dx

are,

respectively.

A) 3, 3 B) 3, 6 C) 3, 9 D) 4, 4

81. If , f x g x and h x are continuous function, thrice differentiable and each satisfythe differential equation

2

20

d y y

dx , then find 1 xφ , where

1 1 1

2 2 2

f x g x h x

x f x g x h x

f x g x h x

φ (here, ,k k f x g x and k h x are the k th

derivatives of

, f x g x and h x , respectively)

A) 0 B) f x g x h x

C) 1 1 1 f x g x h x D) 182. The incentre of the triangle formed by the lines xy=0 and 1

3 4

x y is (h,k) , then

A) (h ,k ) lies on the line x+y = 12

B) (h ,k ) lies on the line x-y =10

C) (h ,k ) lies on the circle 2 2 12 x y

D) (h ,k ) lies on the circle 2 2

4 5 25 x y

83. If the lines1 1 1

2 3 4

x y z and

3

1 2 1

x y k z intersects , then k is equal to

A) 32

B) 92

C) 92

D) 32


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Iit jee Model Paper 4

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