JEE Mains Physics Model Paper 6

Space for rough work

PHYSICS

41. Number of significant figures in 0.00100 and (1.10 104 + 1.11 10

4) respectively are

(a) 3, 7 (b) 5, 7 (c) 3, 3 (d) 5, 3

42. If net charge enclosed by a surface is zero, electric field at every point on the surface

(a) must be zero (b) must be non-zero

(c) may or may not be zero (d) must be perpendicular to surface

43. Which of the following is a wrong description of biding energy of a nucleus?

(a) It is the energy required to break a nucleus in to its constituent nucleons.

(b) It is the energy released when free nucleons combine to form a nucleus.

(c) It is the sum of the rest mass energies of its nucleons minus the rest mass energy of the

nucleus.

(d) It is the sum of the kinetic energy of all the nucleons in the nucleus.

44. Rain is falling with a speed of 20 ms–1

. A man rides a bicycle holds an umbrella making an

angle of 300 with vertical. When he halves his speed, he has to hold the umbrella vertically

for maximum protection. The initial speed of bicycle is

(a) 35 ms–1

(b) 10 ms–1

(c) 310 ms–1

(d) 20 ms–1

45. A ball of mass m strikes a wall with a speed u at an angle of

and reflects back at an angle of as shown in figure. If no

external force acts on the system and ball remains in contact

with wall for time t the average force exerted by wall on the

ball is

(a) t

mu cotcotsin (b)

t

mu cotcotsin

(c) t

mu tantansin (d)

t

mu tantancos

u

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46. A solid disc and a ring of same radius are placed gently on a horizontal rough table

simultaneously with same initial angular speed 0. If coefficient of kinetic friction is same

for both disc and ring, which of the two will start to roll earlier

(a) disc (b) ring

(c) both at the same time (d) they will not roll at all

47. A massless rod PQ of length 50 cm is supported at its

ends by two wires A and B of equal length L as shown

in the figure. The cross sectional area of B is double of

A and Young modulus of elasticity of A is three times

that of B. If block of mass m is attached at a distance of

10 cm from end P, then the ratio of elongation of wire

A and B is

Q

B A

P

L 50cm

R

m 10cm

(a) 6

1 (b)

8

3 (c)

3

2 (d)

3

8

48. The coefficient of linear expansions of a metal rod varies with its absolute temperature as 1–8102 KT . The percentage increase in the length of rod, when heated from 27

0C

to 1270C will be

(a) 0.07 % (b) 0.14% (c) 0.03% (d) 0.015%

49. A U tube of length l contains a liquid. What is the

difference in height between the liquid columns in the

vertical arms if the tube has an acceleration a towards

the right.

(a) 2

2

2g

la (b)

2

2

g

la

(c) g

la2 (d)

g

la

l

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50. The operating temperature of a tungsten filament in an incandescent lamp is T K and its

emissivity is e. The surface area of the filament of a W watt lamp is

(a) 4T

W (b)

4Te

W (c)

Te

W (d)

4T

eW

51. A carnot refrigerator takes heat from water at 00C and rejects heat to a room at 27

0C. If the

50 kg of water at 00C are converted to ice at 0

0C, then the heat rejected to room is (latent

heat of fusion of ice = 80 cal g–1

)

(a) 4.4 106 cal (b) 4 10

6 cal (c) 0.4 10

6 cal (d) 44 10

6 cal

52. The equation of transverse travelling wave in a string is txy 2005.0cos2 , where x

and y are in cm and t is in second. If the mass per unit length of string is 5g cm–1

, then the

tension in string is

(a) 0.8 N (b) 0.08 N (c) 8 N (d) 0.008 N

53. A charge + q is placed at each of the points x = x0, x = 3x0, x = 5x0, ……. on the x-axis, and

a charge – q is placed at each of the points x = 2x0, x = 4x0, …….. Here, x0 is a positive

constant. The potential at the origin due to the above system of charges is

(a) zero (b) 2ln8 00 x

q (c) infinite (d)

004

2ln

x

q

54. What will be percentage change in energy stored in

the capacitor after switch S shown in the figure is

closed.

(a) 20 % decrease (b) 20 % increase

(c) 36 % increase (d) 36 % decrease

1

3

3

1

C

10V

S

55. In the given circuit, the reading of the ammeter is

the same when both switches (S1 and S2) are open

and when both the switches closed. The resistance R

has a value

(a) 900 (b) 600

(c) 450 (d) 100

S1 A

R

100

50 S2

300

1.5V

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56. A long solenoid is having 1000 turns per meter and the current in its winding is increasing

at the rate of 100 As–1

. The cross sectional area of the solenoid is 4 cm2. What is the value

of induced emf in solenoid?

(a) zero (b) 16 V (c) 16 V (d) 8 V

57. In an a.c. circuit V and I are given by, V = 100 sin (100 t) volts, I = 100sin (100t+ /3) mA.

The power dissipated in the circuit is

(a) 104 watt (b) 10 watt (c) 2.5 watt (d) 5.0 watt

58. A microscope is focused on the upper surface of a glass plate. A second plate is then placed

over it. In order to focus the bottom surface of the second plate, the microscope must be

raised 1 mm. In order to focus on the upper surface of second plate it must be raised 2.5 mm

further. The refractive index of second plate is,

(a) 3/2 (b) 7/2 (c) 7/5 (d) 5/3

59. What is the initial activity of a 276 ng sample of 92

Kr (half life 2.079 s) (NA = 6 1023

)

(a) 6 1014

s–1

(b) 9.2 10–8

s–1

(c) 2 1014

s–1

(d) 1.8 1013

s–1

60. In the following, which one of the diodes is reverse biased?

+5V

R

(a)

+10V

R (b)

+5V

–12V

R (c)

–5V

R (d)

–10V

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61. The equation of electric field in a plane electromagnetic wave is given by

iytE ˆ2.01060sin6 6

. The equation of corresponding magnetic field will be given

as

(a) kytB ˆ2.01060sin102 68

(b) iytB ˆ2.01060sin102 68

(c) kytB ˆ2.01060sin102 68

(d) jytB ˆ2.01060sin102 68

62. In figure a conducting bar of mass m, approximate length

b, and resistance R slides down the incline while making

contact with the resistance less U loop at an angle of as

shown in the figure. The terminal speed of the bar as it

slides down in the vertically upward magnetic field B will

be

B

(a) cos22 Bb

mgR (b)

sin22 Bb

mgR (c)

sin

cos22Bb

mgR (d)

222 cos

sin

Bb

mgR

63. A particle starting from rest moves in a straight line such

that its acceleration changes with time as shown in

acceleration-time curve. The displacement of particle

after 9 s will be,

(a) 202.5 m (b) 101.25 m

(c) 97.5 m (d) 30 m

3 6 9

5 a

(m/s

2)

t(s)

64. A uniform rope of length l lies on the table. If the coefficient of friction between the rope

and table is , then the maximum length l1 which can overhang from the edge of the table

without sliding down is

(a) l

(b) 1

l (c)

1

l (d)

1

l

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65. A block of mass m (= 1 kg) resting at a height of

5 m from ground slides down a smooth incline

plane AB and enters a rough horizontal patch BC

of length 2 m. The retarding force f in this patch

BC varies as N5kxf , where k = 10 N/m.

m A

60°

smooth

B C D

rough smooth

5m

2m

What will be kinetic energy of block when it crosses the rough patch BC and reach smooth

horizontal plane CD.

(a) zero (b) 38 J

(c) 19 J (d) it will never reach smooth plane CD

66. A metallic meter bar AB, 1 kg in mass, supported on two knife edges at C and D placed at a

distance of 10 cm and 80 cm from end A respectively. Find out the maximum mass M of a

block to be attached at end B so that bar remains in equilibrium (Assume bar to be of

uniform cross section and homogeneous).

(a) 1 kg (b) 1.5 kg (c) 2 kg (d) 9

4kg

67. Two uniform solid sphere of equal radii R and equal mass M

have a centre to centre separation 8R as shown in figure. The

two spheres are held fixed. A projectile of mass m is

projected from the surface of the one sphere directly towards

the centre of the second sphere. The minimum speed v of the

projectile so that it reaches the surface of the second sphere.

C1 M

A

R C2

M

B

R

8R

m v

(a)

2/1

5

3

R

GM (b)

2/12

R

GM (c)

2/1

R

GM (d)

2/1

7

9

R

GM

68. The flow rate of water from a tap of diameter 4

cm is 3 litre per minute. The coefficient of

viscosity of water is 10–3

Pa s. The nature of flow is,

(a) Laminar (b) Turbulent

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69. On a P-V plot three isotherms are plotted at temperatures T1,

T2 and T3. Cyclic process 1–2–3–4–1 is shown in this plot.

The process 1–2–3–4–1 can be redrawn on P-T diagram as,

P 1 2

3 4

V

P

T

4 3

2 1

(a)

P

T

4 3

2 1

(b)

P

T

4

3

2 1 (c)

P

T

4

1

(d) 3

2

70. A circular hoop of radius R and mass M is hung on a narrow horizontal rod and allowed to

swing in the plane of the hoop. What will be the equivalent length of the simple pendulum

having same time period?

(a) 2

R (b) R (c) 2R (d) R

2

3

71. A string stretched between fixed supports separated by 75 cm has resonant frequencies of

420 Hz and 315 Hz with no intermediate frequencies. The fundamental frequency of the

string is

(a) 52.5 Hz (b) 105 Hz (c) 157.5 Hz (d) 210 Hz

72. An uncharged conducting spherical shell of inner radius a and outer radius b has a positive

point charge Q located at its centre. Which of the following curve will represent electric

field (E) as a function (r) from the centre of shell

E

r

(a)

a b

E

r

(b)

a b

E

r

(c) a b

E

r

(d)

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73. An inductor (L= 100 mH), a resistor (R = 100 ) and a

battery (E = 100 V) are initially connected in series as

shown in the figure. After a long time the battery is

disconnected after short circuiting the points A and B.

The current in the circuit 1 ms after the short circuit is

E

A B

R

L

(a) 1 A (b) 1/e A (c) e A (d) 0.1 A

74. What is baab VVV in the circuit shown, when switch

S is open

(a) +12 V (b) –12 V

(c) +36 V (d) –36 V

a b

3 6

3 6

3 S

V=36V

75. Four very long current carrying wires in the same plane

intersect to form a square of 40 cm side as shown in the

figure. Find the magnitude and direction of current I so

that the magnetic field at the centre of the square is zero

(a) 2A in the direction of current of 10A

(b) 2A in the direction opposite to current of 10 A

(c) 18 A in the direction of current of 10 A

(d) 12 A in the direction opposite to current of 10A

10A I

40cm

8A

20A

76. What will be the change in stopping potential for photoelectron emitted from a surface if the

wavelength of the incident light is reduced from 400 nm to 360 nm.

(a) 0.34 V (b) 3.4 V (c) 34 V (d) zero

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77. The rectangular loop in figure is pivoted about the y-axis

and carries a current of 10A in the direction indicated. If

the loop is in a uniform magnetic field of magnitude 0.2

T parallel to x-axis, the torque required to hold the loop

in the position will be

(a) zero (b) 0.0096 Nm

(c) 0.0083 Nm (d) 0.0048 Nm

X

Z

Y

6cm

8cm

600

10A

B

78. A layer of liquid is placed on the hypotenuse of a prism

as shown in the figure. If the refractive index of the

material of prism is 1.50, find the maximum refractive

index of the liquid so that light ray shown in figure is

totally reflected at hypotenuse

A C

B

90°

60°

Liquid

Incident ray

(a) 1 (b) 1.3 (c) 3 (d) 4/3

79. A square wire loop of side 2 m is lying in the plane of

paper and a time varying magnetic field given by,

05.0B –0.8 t, (B in tesla and t in second) is acting

vertically inwards through half the area of loop as shown

in the figure. The loop contain a 20V battery with

negligible internal resistance. The net emf in the circuit

at t = 0 is

2m 20V

B

(a) 16.8 V (b) 18.4 V (c) 21.6 V (d) 23.2 V

80. A transformer has 500 primary turns and 10 secondary turns. If primary voltage is 120V and

secondary load is 15 , the current in primary and secondary will be (the efficiency of

transformer is 100 %)

(a) 3.2 mA, 0.16 A (b) 3.2 A, 0.16 A (c) 3.2 A, 0.16 mA (d) 3.2 mA, 0.16 mA

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JEE Mains Physics Model Paper 6