Albert Einstein was conferred with the Nobel prize in physics for his work on

Special theory of relativity

Bose – Einstein Statistics

Photoelectric effect

General relativity

A quantity z, to be estimated has a dependency on the variables a, b and c as \(\large z = ab^2c^{-2}\). The percentage of error in the measurement of a, b and c are respectively, 2.1 %, 1.3% and 2.2%. The percentage of error in the measurement of z would then be

5.6%

1.6%

1.0%

9.1%

The nature of a graph drawn for a freely falling body with time on x –axis and speed on the y – axis is ( Assuming initial speed to be zero )

a straight line with positive y – axis intercept.

a straight line passing through the origin.

A parabola

A straight line parallel to y – axis with positive x – axis intercept

A particle A moves along the line, y = 30 m with the constant velocity, v parallel to x – axis. At the moment particle A passes the y – axis, a particle B starts from the origin with zero initial speed and a constant acceleration, \(\large a = 0.40 \ m/sec^2\). The angle between \(\large \underset{a}{\rightarrow}\) and y – axis is 60°. If the particles A and B collide after sometimes, then the value \(\large \left | \underset{v}{\rightarrow} \right |\) will be

2 m/s

3 m/s

4 m/s

5 m/s

A ball moves one-fourth \(\Large (\frac{1^{th}}{4})\) of a circle of radius R in time T. Let  \(\large \nu_1\) and \(\large \nu_2\) be the magnitudes of mean speed and mean velocity vector. The ratio \(\Large \frac{\nu_1}{\nu_2}\) will be

\(\Large \frac{\pi}{2}\)

\(\Large \frac{3}{\pi}\)

\(\Large \frac{2}{\sqrt 3 \pi}\)

\(\Large \frac{\pi}{2\sqrt 2}\)

A 4 kg object has a velocity, \(\large 3.0 \hat i \ m/s\) at some instant. Eight seconds later, its velocity is \(\large (8.0 \hat i+ 10.0\hat j) m/s\) . Assuming that the object is subjected to a constant net force, the magnitude of the force is

\(\Large \frac{5\sqrt 5}{2} N\)

\(\Large \frac{5\sqrt 3}{8} N\)

\(\Large \frac{8\sqrt 5}{3} N\)

\(\Large \frac{10\sqrt 3}{7} N\)

A block of mass 10 kg, initially at rest, makes a downward motion on 45° inclined plane. Then the distance travelled by the block after 2seconds is 
(Assume the coefficient of kinetic friction to be 0.3 and \(\large g = 10 \ ms^{-2}\))

\(\large 7\sqrt 2\) m

\(\Large \frac{9}{\sqrt 2}\) m

\(\large 10\sqrt 2\) m

\(\large 5\sqrt 2\) m

Conservative forces are defined as the force for which,

Work done depends upon only on the initial and final positions.

Work done depends on the initial and final positions and also on the path taken.

Work done depends only on the path taken.

Work done depends only on the initial position.

A rocket motor consumes 100 kg of fuel per second exhausting it with a speed of 5 km/s. The speed of the rocket when its mass is reduced to \(\Large \frac{1}{20^{th}}\) of its initial mass, is (Assume initial speed to be zero and ignored gravitational and viscous forces.)

20 km/s

40 ln (2) km/s

5 ln (20) km/s

10 ln (10) km/s

Ball A of mass 50 gm and speed 10 m/s collides with other ball B of mass 10 gm and speed 15 m/s travelling in opposite direction with each other. Determine the final speed of ball B, if the coefficient of restitution is \(\Large \frac{2}{5}\).
 

\(\Large \frac{40}{3} \ m/s\)

\(\Large \frac{75}{3} \ m/s\)

\(\Large \frac{91}{8} \ m/s\)

\(\Large \frac{85}{6} \ m/s\)

A solid sphere of mass 5 kg rolls on a plane surfaces. Find its kinetic energy at an instant when its centre moves with speed 4 m/s.

56 J

45 J

75 J

105 J

A body of mass 0.3 kg hangs by a spring with a force constant of 50 N/m. The amplitude of oscillations is damped and reaches \(\Large \frac{1}{e}\) of its original value in about 100 oscillations. If ω and ω′ are the angular frequencies of undamped and damped oscillations respectively, then percentage of \(\Large (\frac{\omega -\omega'}{\omega})\) is

\(\Large (\frac{1}{800\pi})\)

\(\Large (\frac{\pi^2}{600})\)

\(\Large (\frac{1}{800\pi^2})\)

\(\Large (\frac{\pi}{400})\)

If a planet of mass \(\large 6.4 \times 10^{23} kg\) can be compressed into a sphere such that the escape velocity from its surface is \(\large 8 \times 10^{4} m/s\), then what should be the radius of the sphere? (Gravitational constant, \(\large G = 6.6 \times 10^{-11} Nm^{-2} kg^{-2}\))

40.4 km

13.2 km

20.4 km

6.8 km

A horizontal aluminum rod of diameter 4 cm projected 6 cm from the wall. An object of mass 400 π kg is suspended from the end of the rod. The shearing modulus of aluminum is \(\large 3.0 \times 10^{10} \ N/m^2\).  The vertical deflection of the end of the rod is ( \(\large g=10 \ m/s^2\)).

0.01 mm

0.02 mm

0.03 mm

0.04 mm

A water tank kept on the ground has an orifice of 2 mm diameter on the vertical side. What is the minimum height of water above the orifice for which the output flow of water is found to be turbulent? (Assume, \(\large g=10 \ m/s^2, \rho_{water} =10^3 kg/m^3\), viscosity = 1 centi – poise)

3 cm

4 cm

6 cm

2 cm

11 cm

A copper ball of radius 3.0 mm falls in an oil tank of viscosity 1 kg/ms. Then, the terminal velocity of the copper ball will be (Density of oil = \(\large 1.5 \times 10^3 \ kg/m^3\), Density of copper = \(\large 9 \times 10^3 \ kg/m^3\) and g = \(\large g=10 \ m/s^2\) )

\(\large 18 \times 10^{-2} m/s\)

\(\large 25 \times 10^{-2} m/s\)

\(\large 15 \times 10^{-2} m/s\)

\(\large 20 \times 10^{-2} m/s\)

The wavelength of the radiation emitted by a black body is 1 mm and Wien’s constant is \(\large 3 \times 10^{-3} mK\). Then the temperature of the black body will be

3 K

30 K

300 K

3000 K

A hot body placed in air cools down to a lower temperature. The rate of decrease of temperature is
proportional to the temperature difference from the surrounding. The body loses 60% and 80% of maximum heat it can loose in time \(\large t_1\) and \(\large t_2\) respectively. The ratio \(\Large \frac{t_2}{t_1}\) will be

\(\Large \frac{ln(10)}{ln(2)}\)

\(\Large \frac{ln(8)}{ln(6)}\)

\(\Large \frac{ln(1)}{ln(3)}\)

\(\Large \frac{ln(5)}{ln(\frac{5}{2})}\)

A Carnot engine with efficiency η operates between two heat reservoirs with temperatures \(\large T_1\) and \(\large T_2\), where \(\large T_1 > T_2\) . If only \(\large T_1\) is changed by 0.4%, the change in efficiency is \(\large \Delta \eta_1\), whereas if only \(\large T_2\) is changed by 0.2%, the efficiency is changed by \(\large \Delta \eta_2\). The ratio \(\Large \frac{\Delta \eta_1}{\Delta \eta_2}\) is approximately,

-2

-4

+3

+4

2

An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by 2 times the initial rms speed. If the initial gas temperature is 27°C, then the final temperature of the ideal gas is

1200 °C

927 °C

827 °C

1473 °C

Consider two tuning forks with natural frequency 250 Hz. One is moving away and another is moving towards a stationary observer at same speed. If the observer hears beats of frequency 5 Hz, then the speed of the tuning fork is: (Given, speed of sound wave is 350 m/s.)

2.5 m/s

3.5 m/s

5.0 m/s

2.0 m/s

A drone fitted with siren in flying directly away from the drone operator and towards a distant building at a speed of 15 m/s. The siren produces sound of frequency 780 Hz. What is the frequency that the operator hears in the echo reflected from the building? [Speed of sound is 340 m/s.]

766 Hz

800 Hz

816 Hz

840 Hz

A point object O is placed on the axis of a cylindrical piece of glass of refractive index 1.6 as shown in the figure. One surface of the glass piece is convex with radius of curvature 3 mm. The point appeared to be at 5 mm on the axis when viewed along the axis and from right side of convex surface. The distance of the point object from the convex surface is:

4 mm

6 mm

3 mm

2.5 mm

The limit of resolution of a telescope is \(\large 2.5 \times 10^{-7}\) radians. If the telescope is used to detect light of wavelength 500 nm coming from a star, the diameter of the objective lens used by telescope is

244 cm

258 cm

228 cm

264 cm

A non-conducting solid sphere has radius R and uniform charge density. A spherical cavity of radius \(\Large \frac{R}{4}\) is hollowed out of the sphere. The distance between center of sphere and center of cavity is \(\Large \frac{R}{2}\). If the charge of the sphere is Q after the creation of the cavity and the magnitude of electric field at the center of the cavity is \(\Large E = K(\frac{Q}{4\pi \epsilon_0 R^2})\) , determine the approximate value of K.

0.32

0.78

0.51

0.45

A metal plate of thickness 2 mm and area \(\large 36 \pi \ cm^2\)  is slid into a parallel plate capacitor of plate spacing 6 mm and area \(\large 36 \pi \ cm^2\). The metal plate is at a distance 3 mm from one of the plates. What is the capacitance of this arrangement?

(Let \(\Large \frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \ Nm^2 C^{-2}\))

8 pF

15 pF

25 pF

20 pF

For the circuit shown in the figure, calculate the resistance between the points A and B.

0.5 R

R

15 R

\(\Large \frac{6}{5}R\)

If the resistance are chosen for the circuit shown in figure in such a way that no current flows through the battery with emf \(\large E_1\), the voltage \(\large V_2\) across \(\large R_2\) and the current \(\large I_3\) flowing through \(\large R_3\) are respectively,

\(\Large V_2 = -4V, I_3 = \frac{5}{2}A\)

\(\Large V_2 = +4V, I_3 = \frac{5}{2}A\)

\(\large V_2 = -3V, I_3 = 1A\)

\(\large V_2 = +3V, I_3 = 2A\)

A semi circular loop of radius 30 cm wire carries current 6 A. An uniform magnetic field 0.5 T is present perpendicular to the plane of the loop. What is the magnitude of force exerted on the wire?

0.9 N

1.8 N

0.8 N

1.4 N

A dielectric circular disc of radius R carries a uniform surface charge density σ. If it rotates about its axis with the angular velocity ω, the magnetic field at the centre of the disc is :

\(\Large \frac{\mu_0 \sigma \omega R^2}{2\pi}\)

\(\Large \frac{\mu_0 \sigma \omega R}{2}\)

\(\Large \frac{\mu_0 \sigma \omega \pi R^2}{4}\)

\(\Large \frac{\mu_0 \sigma \omega R}{2\sqrt2}\)

The earth’s magnetic field at the geometric poles is \(\large \sqrt{10} \times 10^{-5} \ T\). The magnitude of the field at a point on the earth’s surface where the radius makes an angle θ with the axis of earth’s assumed magnetic dipole is \(\large 5 \times 10^{-5} \ T\) . The magnitude of θ in degree is 

30°

60°

45°

75°

Consider a current in a circuit falls from 6.0 A to 1.0 A in 0.2 s. If an average emf of 150 V is induced by the circuit, then the self inductance of the circuit is

2 H

6 H

4 H

8 H

A series of LCR circuit with L = 0.5 H and R = 10 Ω is connected to an AC supply with rms voltage and frequency equal to 200 V and \(\Large \frac{150}{\pi}\)Hz respectively. The magnitude of the capacitance is varied so that current amplitude in the circuit becomes maximum. The rms voltage difference across the inductor is

3000 V

2500 V

2000 V

2600 V

The magnetic field of an electromagnetic- wave obeys the relation in a certain region is \(\large B = 10^{-12} sin (5 \times 10^6 t) T\), where t is the time. Then, the induced emf, in a 300 turns in coil of area \(\large 20 \ cm^2\) oriented perpendicular to the field is 

\(\large -2 \times 10^{-5} cos (5 \times 10^6 t) \ V\)

\(\large -3 \times 10^{-6} cos (5 \times 10^6 t) \ V\)

\(\large -2.5 \times 10^{-6} cos (5 \times 10^6 t) \ V\)

\(\large -3.3 \times 10^{-6} cos (5 \times 10^6 t) \ V\)

The wavelength of a charged particle of mass \(\large 8.0 \times 10^{-31} kg\), charge \(\large 1.6 \times 10^{-19} C\) and the kinetic energy 3 keV will be ( Let \(\large h = 6.4 \times 10^{-34} Js\) )

0.4 Å

2.1 Å

1.0 Å

0.1 Å

Let \(\large \lambda_P\) and  \(\large \lambda_L\) be the longest wavelengths observed in the Paschen and Lyman series respectively. Choose the correct option

\(\Large 4 < \frac{\lambda_P}{\lambda_L} < 6\)

\(\Large 7 < \frac{\lambda_P}{\lambda_L} < 8\)

\(\Large 15 < \frac{\lambda_P}{\lambda_L} < 16\)

\(\Large 30 < \frac{\lambda_P}{\lambda_L} < 32\)

A radioactive nucleus can decay in two different processes with half life 0.7 hr and 0.3 hr. The effective average life of the nucleus in minutes approximately is (Let ln 2 = 0.7)

14

18

24

26

Assertion (A): Si and GaAs are the preferred materials for solar cells.

Reason (R): Both these materials have energy band gaps much below the energy level corresponding to the maximum solar irradiance in the solar spectrum.

The correct answer is

(A) is correct but (R) is incorrect.

Both (A) and (R) are correct and (R) is the correct explanation of (A).

Both (A) and (R) are correct and (R) is not the correct explanation of (A).

Both (A) and (R) are incorrect.

The truth table of logic gate is given below, then identify the gate

NOT gate

OR gate

AND gate

NAND gate

A transmitting antenna has a height 20m. What will be the height of receiving antenna, if the maximum distance between them for the satisfactory communication in the line of sight (LOS) mode is 40 km? ( The earth radius is 6400 km)

25 m

30 m

60 m

45 m