Physics

Single correct answer type:

1. The displacement of a particle varies with time as where

are positive constants. The velocity of the particle will

(A) Decrease with time

(B) Be independent of and

(C) Drop to zero when

(D) Increase with time

Solution: (D)

Given,

We know that, velocity,

( )

Where,

The value of term increases and of term increases with time.

As a result, velocity goes on increasing with time.

2. A transformer having efficiency of 75% is working on 220V and 4.4kW power supply.

If the current in the secondary coil is . What will be the voltage across secondary coil

and the current in primary coil?

(A) (B)

(C) (D)

Solution: (C)

Given,

We know that,

Efficiency,

Percentage efficiency

3. A fish rising vertically to the surface of water in a lake uniformly at the rate of 2m/s

observes a kingfisher diving vertically towards the water at a rate of 10m/s. If refractive

index of water

what will be the actual velocity of the kingfisher

(A) 10 m/s (B) 8 m/s (C) 6 m/s (D) 9 m/s

Solution: (C)

Velocity of bird w.r.t. fish,

⁄

and velocity of fish w.r.t. ground

⁄

Distance between bird and fish, as seen by fish

on differentiating w.r.t. time, we get

⁄

4. One mole of a monoatomic ideal gas undergoes the process in the given p –V

diagram. The molar heat capacity for this process is

(A)

(B)

(C)

(D)

Solution: (B)

Area under p -V diagram

( )

(

)

Thus,

Molar heat capacity,

⁄

⁄

5. A pan with a set of weights is attached to a light spring. The period of vertical

oscillation is 0.5s. When some additional weights are put in pan, then the period of

oscillations increases by 0.1s. The extension caused by the additional weight is

(A) 5.5 cm (B) 3.8 cm (C) 2.7 cm (D) 1.3 cm

Solution: (C)

Give,

We know that, √

√

√

On squaring both sides, we get

……(i)

√

√

(

)

(

)

[using equation (i)]

( )

…….(ii)

[using equation (ii)]

6. A cylinder of radius R and length L is placed in a uniform electric field E parallel to the

cylinder axis. The total flux for the surface of the cylinder is given by

(A) (B)

(C)

(D)

Solution: (D)

Flux through surface

Flux through curved surface, ∫

∫

Total flux through cylinder

7. If and that is perpendicular to What is the angle between and . If

| | | |?

(A)

(B)

(C)

(D)

Solution: (C)Given,

and

Since, , therefore

Also, | | | |, therefore

√

Now,

√

This gives

8. A beam of light travelling along axis is described by the electric field

(

) the maximum magnetic force on a charge moving along Y –

axis with the speed of ⁄ is

(A) (B)

(C) (D) None of these

Solution: (B)

Given, electric field,

(

) ……(i)

We know that,

(

) …..(ii)

On comparing equations (i) and (ii), we get

⁄ ⁄

Maximum magnetic field,

9. A body is whirled in a horizontal circle of radius 25cm. It has an angular velocity of 13

rad/s. What is its linear velocity at any point on circular path?

(A) 2 m/s (B) 3 m/s (C) 3.25 m/s (D) 4.25 m/s

Solution: (C)

Given,

⁄

Linear speed = Radius Angular speed

Or

⁄

10. In the given figure, potential difference between A and B is

(A) 0 (B) 5 V (C) 10 V (D) 15 V

Solution: (C)

Equivalent resistance,

Hence, potential difference between A and B.

(

)

11. A block having 12g of element is placed in a room. This element is radioactive

element with half-life of 15 years. After how many years will there be just 1.5g of the

element in the box?

(A) 40 year (B) 45 year (C) 20 year (D) 15 year

Solution: (B)

Given,

(

)

(

)

(

) [

]

(

)

12. In the given figure what will be the coefficient of mutual inductance

(A)

(

) (B)

(

)

(C)

(

) (D)

(

)

Solution: (C)

Magnetic field due to wire

and

On integrating both sides, we get

∫ ∫

∫

|

[ ( ) ]

* (

)+

Where, M = coefficient of mutual inductance

(

)

13. An L-C-R series circuit with a resistance of is connected to 200 V (AC source)

and angular frequency 300 rad/s. When only the capacitor is removed, then the current

lags behind the voltage by . When only the inductor is removed the current leads the

voltage by . The average power dissipated in original L-C-R circuit is

(A) 50 W (B) 100 W (C) 200 W (D) 400 W

Solution: (D)

Given, ⁄

Phase angle,

√

i.e., √ (√ √ )

So, average power,

14. The intensity of each of the two slits in Young’s double slit experiment is

Calculate the minimum separation between the points on the screen, where intensities

are and . If fringe width is b

(A)

(B)

(C)

(D)

Solution: (C)

We know that, intensity,

<b>Case I:</b>

*

+

…….(i)

<b>Case II:</b>

*

+

……(ii)

[given]

15. A metal rod at a temperature of , radiates energy at a rate of 17W. If its

temperature is increased to , then it will radiate at the rate of

(A) 49.6 W (B) 17.5 W (C) 50.3 W (D) 67.5 W

Solution: (A)

Given, initial temperature of metal rod ( )

Rate of radiated energy ( )

Final temperature ( )

We know, from the Stefan’s law,

Or

(

)

(

)

Therefore, final radiated energy,

16. Two wires are stretched through same distance. The force constant of second wire

is half as that of the first wire. The ratio of work done to stretch first wire and second

wire will be

(A) 2 : 1 (B) 1 : 2 (C) 3 : 1 (D) 1 : 3

Solution: (A)

As

If both wires are stretched through same distance, then

It is given that

17. A square wire of side 2.0cm is placed 20cm in front of a concave mirror of focal

length 10cm with its centre on the axis of the mirror and its plane normal to the axis.

The area enclosed by the image of wire is

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

Solution: (D)

Given, square wire offside = 2cm.

Area of second wire = ?

( )

We know that,

( )

( )

18. A lead bullet penetrates into a solid object and melts. Assuming that 50% of its

kinetic energy was used to heat it, the initial speed of the bullet is (the initial temperature

of the bullet is and its melting point is ). Latent heat of fusion of lead

⁄ and specific heat capacity of lead ⁄

(A) ⁄ (B) ⁄ (C) ⁄ (D) ⁄

Solution: (B)

Given, ⁄

⁄ then

( )

⁄

⁄

19. A quarter cylinder of radius R and refractive index 1.5 is placed on a table. A point

object P is kept at a distance of mR from it as shown in figure. For what value of m for

which a ray from P will emerge parallel to the table?

(A)

(B)

(C)

(D)

Solution: (C)

Refraction at plane surface (1),

Using formula,

for plane surface.

( )

Refraction at spherical surface (2)

(

)

* ( )+

( )

20. The graph

and stopping potential ( ) of three metals having work function

and in an experiment of photoelectric effect is plotted as shown in the figure. Which

one of the following statement is/are correct? [Here is the wavelength of the incident

ray]

(i) Ratio of work functions

(ii) Ratio of work functions

(iii)

, where h = Planck’s constant, c = speed of light

(iv) The violet colour-light can eject photoelectrons from metals 2 and 3

(A) (i), (iii) (B) (i), (iv) (C) (ii), (iii) (D) (i), (ii) and (iv)

Solution: (A)

According to Einstein photoelectric equation,

[

]

graph is a straight line.

Slope,

The curves intersect the

axis, where is zero.

For metal 1 For metal 2 For meta 3

For metal 2, threshold wavelength,

Similarly,

So for metal 1, for metal 3

Thus, violet light will eject photoelectron for metal 2 and not metal 3.

21. The concentric, conducting spherical shells and with radii and

respectively. and are connected by a conducting wire and is uniformly charged to

charge as shown in figure. Charges on shells and will be

(A)

(B)

(C)

(D)

Solution: (B)

Let charges on and be and

By conservation of charge,

[

]

[

]

Since, and are connected.

22. The temperature of a gas is raised from to . The root mean square speed

(A) Gets halved

(B) Gets doubled

(C) Is √(

) times the earlier value

(D) Remains the same

Solution: (B)

Given,

√(

)

√

( ) ( )

√

( ) ( )

√

( ) ( )

23. A particle slides down on a smooth incline of inclination , fixed in an elevator

going up with an acceleration ⁄ The box of incline has length 4m. The time taken

by the particle to reach the bottom will be

(A)

√ (B)

√ (C)

√√

(D)

√√

Solution: (C)

In the frame of elevator,

a = acceleration of the particle with respect to the elevator

( )

( )

( )

⁄

The distance travelled by the particle from the top to the bottom,

√

√

Using

,

√

√

√√

24. A stone projected with a velocity u at an angle with the horizontal reaches

maximum height When it is projected with velocity u at an angle (

) with the

horizontal, it reaches maximum height . The relation between the horizontal range R

of the projectile, and is

(A) √ (B) ( )

(C) ( ) (D)

Solution: (A)

We known that,

and ( )

( )

[ ]

√

25. Two batteries of emf 3V and 6V with internal resistances and are connected

in a circuit with resistance of as shown in figure. The current and potential

difference between the points P and Q are

(A)

(B)

(C)

(D)

Solution: (D)

Applying Kirchhoff’s voltage law in the given loop,

potential difference across

26. A light string passes over a frictionless pulley. To one of its ends a mass of 8 kg is

attached. To its other end two masses of 7kg each are attached. The acceleration of the

system will be

(A) 10.2 g (B) 5.10 g (C) 20.36 g (D) 0.27 g

Solution: (D)

From free body diagram of body A,

…..(i)

For body B,

…..(ii)

For body C,

……(iii)

On solving equations (i), (ii) and (iii), we get

[( ) ]

As,

27. A capillary tube of length L and radius is connected with another capillary tube of

the same length but half the radius in series. The rate of steady volume flow of water

through first capillary tube under a pressure difference of p is V. The rate of steady

volume flow through the combination will be (the pressure difference across the

combination is p)

(A) (B)

(C)

(D)

Solution: (C)

Problems of series and parallel combination of pipes can be solved in the similar

manner as is done in case of an electrical circuit. The only difference is potential

difference is replaced by and electrical resistance as,

And

(

)

Electric current is replaced by rate of volume flow V’.

……(i)

( ) ( )

…….(ii)

From equations (i) and (ii) we get

28. A system consist of a cylinder surrounded by a cylindrical shell. A cylinder is a

radius R and is made of material of thermal conductivity K, whereas a cylindrical shell

has inner radius R and outer radius 2R and is made of material of thermal conductivity

twice as that of cylinder. Assuming the system in steady state and negligible heat loss

across the cylindrical surface, find the effective thermal conductivity of the system are

maintained at two different temperatures.

(A) (B)

(C)

(D)

Solution: (C)

and

( )

and are in parallel.

On putting values of and , we get

( ) [ ]

29. An isotropic point source emits light with wavelength 500 nm. The radiation power of

the source is Find the number of photons passing through unit area per

second at a distance of 3m from the source.

(A) ⁄ (B) ⁄

(C) ⁄ (D) ⁄

Solution: (B)

Given,

As,

……(i)

Where, is number of photons per second. At distance from point source, number of

photons/area/time

[from equation (i)]

( )

⁄

30. If a proton and anti-proton come close to each other and annihilate, how much

energy will be released?

(A) (B)

(C) (D)

Solution: (B)

Mass of proton = mass of anti-proton

Energy equivalent to amu = 931 MeV.

So, energy equivalent to 2 amu MeV

31. A body at rest slides down a inclined plane. The time taken by it to slide down is

twice the time it takes when it slides down the same distance in the absence of friction.

The coefficient of friction between the body and the inclined plane is

(A) 0.43 (B) 0.37 (C) 0.64 (D) 0.75

Solution: (A)

When a plane is inclined to the horizontal at an angle which is greater than the angle

of repose, then the body placed on the inclined plane slides down with an acceleration

a.

From figure,

……(i)

Net force on the body down the inclined plane

……(ii)

i.e., *

+

[From equation (i)]

( )

( )

Time taken by the body to slide down the plane

√

√

( )

√

[In absence of friction]

[Given]

|√

( )|

|√

|

( )

32. A bat emitting an ultrasonic wave of frequency at speed of ⁄

between two parallel walls. The two frequencies heared by the bat will be

(A)

(B)

(C)

(D)

Solution: (B)

Frequency received by bat after reflection from wall (1),

[

]

*

+ [given, ]

Frequency received by bat after reflection from wall (2),

*

+

[

]

33. The charge on two spheres are and respectively. They experience a

force F. If reach of them is given an additional charge of then the new force of

attraction will be

(A) (B)

(C)

√ (D)

Solution: (A)

Given,

New force

We know that,

( ) ( )

( ) ( )

34. A rod made up of metal is 1.2m long and 0.8 cm in diameter. Its resistance is

. Another disc made of the same metal is 2.0 cm in diameter and 1.25 mm

thick. What is the resistance between the round faces of the disc?

(A) (B)

(C) (D)

Solution: (C)

Given,

thickness = 1.25 mm,

Resistivity of the material of the rod

( )

Resistance of disc, ( )

( )

( )

35. A body is moving along a rough horizontal surface with an initial velocity of

If the body comes to rest after travelling a distance of 12m, then the coefficient of sliding

friction will be

(A) 0.5 (B) 0.2 (C) 0.4 (D) 0.6

Solution: (C)

Given,

By third equation of motion,

( )

Coefficient of sliding friction is given by

36. The magnification produced by a astronomical telescope for normal adjustment is

10 and the length of the telescope is 1.1m. The magnification, when the image is

formed atleast distance of distinct vision is

(A) 6 (B) 18 (C) 16 (D) 14

Solution: (D)

Given, m = 10, length of telescope = 1.1m

We know that,

Magnification,

[ ]

( )

Magnification least distance of distinct vision,

( )

(

) [ ]

37. A circular current carrying coil has a radius R. The distance from the ceentre of the

coil, on the axis, where B will be

of its value at the centre of the coil is

(A)

√ (B) √ (C) √ (D)

√

Solution: (B)

( )

[

]

(

)

*

+

(

)

*

+

(

)

√

38. Angular width of central maximum in the Fraunhoffer diffraction pattern of a slit is

measured. The slit is illuminated by light of wavelength . When the slit is

illuminated by light of another wavelength, then the angular width decreases by 30%.

The same decrease in angular width of central maximum is obtained when the original

apparatus is immersed in a liquid. The refractive index of the liquid will be

(A) 1.25 (B) 1.42 (C) 1.67 (D) 1.5

Solution: (B)

Given,

Angular width of central maximum

and

From equations (i) and (ii), we get

When immersed in liquid,

*

+

39. An energy of 68.0 eV is required to excite a hydrogen-like atom in its second Bohr

energy level to third energy level the charge of nucleus is Ze. The wavelength of a

radiation required to eject the electron from first orbit to infinity is

(A) 2.2 nm (B) 2.85 nm (C) 3.2 nm (D) 2.5 nm

Solution: (D)

Given, and

The difference in energies of two orbits

*

+

Where,

[

]

[

]

[

]

Wavelength of photo,

*

+

[

]

40. A current carrying loop is placed in a uniform magnetic field in four different

orientations I, II, III and IV as shown in figure. Arrange them in decreasing order of

potential energy.

(A) (B)

(C) (D)

Solution: (C)

As we know that, potential energy of a magnet in a magnetic field

Where, m = magnetic dipole moment of the magnet B = magnetic field

<b>Case I:</b>

[ ]

<b>Case II:</b>

[ ]

<b>Case III:</b> is acute angle

( )

Thus,

<b>Case IV:</b> is obtuse

( )

( )

Thus,

Therefore, decreasing order of PE is

41. Two different isotherms representing the relationship between pressure p and

volume V at a given temperature of the same ideal gas are shown for masses and

, then

(A) Nothing can be predicted (B)

(C) (D)

Solution: (B)

For

…..(i)

For

……(ii)

From equations (i) and (ii), we get

Thus,

42. target is bombarded with a proton beam current of A for one hour to

produce of activity disintegrations per second. Assuming that one

radioactive nuclei is produced by bombarding 1000 protons, its half-life is

(A) (B)

(C) (D)

Solution: (A)

Given,

We know that,

Number of protons

[ ]

Number of nuclei produced

Activity of disintegration/s

Activity,

[

]

43. In the given figure, the capacitors have a capacitance each. If the

capacitor has a capacitance then effective capacitance between A and B will

be

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

Solution: (C)

When a battery is applied across A and B, then the points b and c will be at the same

potential

( )

Therefore, no charge flows through

As and are in series.

Their equivalent capacitance,

Similarly, and are in series. Therefore, their equivalent capacitance

Now, and are in parallel. Therefore, effective capacitance between A and B

44. The truth table for the following logic circuit is

(A) ||

|| (B) ||

||

(C) ||

|| (D) ||

||

Solution: (A)

The truth table for the given logic circuit is

0 0 1 1 0 0 0

0 1 1 0 1 0 1

1 0 0 1 0 1 1

1 1 0 0 0 0 0

45. A sphere of mass m moving with velocity hits inelastically with another stationary

sphere of same mass. The ratio of their final velocities will be (in terms of e)

(A)

(B)

(C)

(D)

Solution: (B)

As coefficient of restitution,

……(i)

By conservation of momentum,

Momentum before collision = Momentum after collision

……(ii)

On solving equations (i) and (ii), we get

( )

( )

46. A small spherical drop fall from rest in viscous liquid. Due to friction, heat is

produced. The correct relation between the rate of production of heat and the radius of

the spherical drop at terminal velocity will be

(A)

(B)

(C)

(D)

Solution: (D)

Viscous force acting on spherical drop

Terminal velocity,

( )

Where, coefficient of viscosity of liquid

density of material of spherical drop

density of liquid

Power imparted by viscous force = Rate of production of heat

(

( )

)

47. A galvanometer of resistance shows a deflection of 5 divisions when a current

of 2 mA is passed through it. If a shunt of is connected and there are 20 divisions on

the scale, then the range of the galvanometer is

(A) 1 A (B) 58 A (C) 58 mA (D) 30 mA

Solution: (C)

There are 20 divisions on scale.

Initially, current for 20 divisions

(

) (

)

48. The total charge induced in a conducting loop when it is moved in magnetic field

depends on

(A) The rate of change of magnetic flux

(B) Initial magnetic flux only

(C) The total change in magnetic flux

(D) Final magnetic flux only

Solution: (C)

Induced emf is given by

As,

Total charge induced ∫

∫

∫

∫

( )

Thus, the induced charge in a conducting loop, moving in a magnetic field depends on

the total change in magnetic flux.

49. Particles of masses are placed on the same line at distance

from The distance of centre of mass from is

(A) ( )

(B)

( ) (C)

( )

(D)

( )

Solution: (D)

L

( )

( )

∑

∑

( ) ( )

( )

( )

50. The length of a given cylindrical wire is increased by 150%. Due to the consequent

decrease in diameter the change in the resistance of the wire will be

(A) 200% (B) 525% (C) 300% (D) 400%

Solution: (B)

If suppose initial length, then

(

)

(

)

51. An ideal solenoid having 5000 turns/m has an aluminium core and carries a current

of 5A. If , then the magnetic field developed at centre will be

(A) 0.031 T (B) 0.048 T (C) 0.027 T (D) 0.050 T

Solution: (A)

Given, ⁄

As, ( )

Where,

⁄

And

⁄

( )

( )

52. A ball of radius R rolls without slipping. Find the fraction of total energy associated

with its rotational energy, if the radius of the gyration of the ball about an axis passing

through its centre of mass is K.

(A)

(B)

(C)

(D)

Solution: (A)

Kinetic energy of rotation is

Where, k is radius of gyration.

Kinetic energy of translation is

Thus, total energy,

(

)

( )

Hence,

( )

53. A capacitor is charged and then made to discharge through a resistance. The time

constant is . In what time will the potential difference across the capacitor decrease by

10%?

(A) (B) (C)

(D)

Solution: (C)

As, we know that

According to the question,

54. A body of mass 2m is placed on earth’s surface. Calculate the change in

gravitational potential energy, if this body is taken from earth’s surface to a height of h,

where h = 4R.

(A)

(B)

(C)

(D)

Solution: (C)

Potential energy,

[ ]

At earth’s surface,

Now, if a body is taken to height, h = 4R, then the potential energy is given by

[ ]

Thus, change in gravitational potential energy,

[ ]

55. The slope of isothermal and adiabatic curves are related as

(A) Isothermal curve slope = adiabatic curve slope

(B) Isothermal curve slope adiabatic curve slope

(C) Adiabatic curve slope isothermal curve slope

(D) Adiabatic curve slope

isothermal curve slope

Solution: (C)

For isothermal process pV = constant

(

)

slope of isothermal curve

For adiabatic process, constant

(

)

slope of adiabatic curve

Clearly, (

)

(

)

56. A solid sphere of mass M and radius 2R rolls down an inclined plane of height

without slipping. The speed of its centre of mass when it reaches the bottom is

(A) √

(B) √ (C) √

(D) √

Solution: (C)

When solid sphere rolls down on an inclined plane, then it has both rotational and

translation kinetic energy

Or

Where, moment of inertia of solid sphere

(

( ) )

[ ]

(

)

[ ]

Now, gain in KE = loss in PE

√

57. A liquid of density ⁄ is filled in a cylindrical vessel upto a height of 3m.

This cylindrical vessel stands on a horizontal plane. There is a circular hole on the side

of the vessel. What should be the minimum diameter of the hole to move the vessel on

the floor, if plug is removed. Take the coefficient of friction between the bottom of the

vessel and the plane as 0.5 and total mass of vessel plus vessel as 95 kg.

(A) 0.107 m (B) 0.053 m (C) 0.206 m (D) 0.535 m

Solution: (A)

Given, ⁄

Let area of hole be a

Reaction force, [ √ ]

And

√

58. The transfer ratio of a transistor is 50. The input resistance of the transistor when

used in the common emitter configuration is The peak value of the collector AC

current for an AC input voltage of 0.02 V peak is

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

Solution: (D)

Given,

Input current,

Also, current gain,

59. The volume of an ideal gas is doubled in an isothermal process. Then, which of the

following is true?

(A) Work done by the gas is positive

(B) Work done by the gas is negative

(C) Internal energy of the system decreases

(D) Internal energy of the system increases

Solution: (A)

For isothermal process,

Work done ( )

[ ]

60. A prism of a certain angle deviates the red and blue rays by 8 and 12, respectively.

Another prism of the same angle deviates the red and blue rays by 10 and 14,

respectively. The prisms are small angled and made of different materials. The

dispersive power of the materials of the prisms are in the ratio

(A) 5 : 6 (B) 9 : 11 (C) 6 : 5 (D) 11 : 9

Solution: (C)

For prism 1.

[ ]

For prism 2,

[ ]

So,