Question 1:

A light string passing over a smooth light fixed pulley connects two blocks of masses m₁ and m₂. If the acceleration of the system is g/8, then the ratio of masses is:

1. 9/7
2. 8/1
3. 4/3
4. 5/3

Question 2:

A uniform magnetic field of 2×10⁻³ T acts along the positive Y-direction. A rectangular loop of sides 20 cm and 10 cm with a current of 5 A is in the Y-Z plane. The current is in the anticlockwise sense with reference to the negative X-axis. Magnitude and direction of the torque is:

1. 2 × 10⁻⁴ N-m along positive Z-direction
2. 2 × 10⁻⁴ N-m along negative Z-direction
3. 2 × 10⁻⁴ N-m along positive X-direction
4. 2 × 10⁻⁴ N-m along positive Y-direction

Question 3:

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is ___%. The value of N is:

1. 4
2. 8
3. 6
4. 5

Question 4:

Force between two point charges q₁ and q₂ placed in vacuum at r cm apart is F. Force between them when placed in a medium having dielectric constant K = 5 at r/5 cm apart will be:

1. F/25
2. 5F
3. F/5
4. 25F

Question 5:

An AC voltage V = 20 sin(200πt) is applied to a series LCR circuit which drives a current I = 10 sin(200πt + π/3). The average power dissipated is:

1. 21.6 W
2. 200 W
3. 173.2 W
4. 50 W

Question 6:

A current of 200 µA deflects the coil of a moving coil galvanometer through 60°. The current to cause deflection through π/10 radians is:

1. 30 µA
2. 120 µA
3. 60 µA
4. 180 µA

Question 7:

The atomic mass of 6C¹² is 12.000000 u and that of 6C¹³ is 13.003354 u. The required energy to remove a neutron from 6C¹³, if the mass of the neutron is 1.008665 u, will be:

1. 62.5 MeV
2. 6.25 MeV
3. 4.95 MeV
4. 49.5 MeV

Question 8:

A ball suspended by a thread swings in a vertical plane so that its acceleration in the extreme and lowest position are equal. The angle (θ) of deflection in the extreme position is:

1. tan⁻¹(√2)
2. 2tan⁻¹(1/2)
3. tan⁻¹(1/2)
4. 2tan⁻¹(1/√5)

Question 9:

Three voltmeters are joined as shown. When a potential difference is applied across A and B, their readings are V₁, V₂, and V₃. Choose the correct option:

1. V₁ = V₂
2. V₁ = V₃ − V₂
3. V₁ + V₂ > V₃
4. V₁ + V₂ = V₃

Question 10:

The total kinetic energy of 1 mole of oxygen at 27°C is:

1. 6845.5 J
2. 5942.0 J
3. 6232.5 J
4. 5670.5 J

Question 11:

Given that the angular speed of the moon in its orbit about the earth is greater than that of the earth around the sun, identify the reason.

1. Shorter period of orbit
2. Larger radius
3. Higher mass of the moon
4. Higher gravitational pull

Question 12:

The primary side of a transformer is connected to 230 V, 50 Hz supply with a turns ratio of 10:1. Load resistance is 46 Ω. The power consumed is:

1. 12.5 W
2. 10 W
3. 11.5 W
4. 12 W

Question 13:

During an adiabatic process, the pressure of a gas is proportional to the cube of its absolute temperature. The ratio of Cp/Cv is:

1. 5/3
2. 3/2
3. 7/5
4. 9/7

Question 14:

The threshold frequency of a metal with work function 6.63 eV is:

1. 16 × 10¹⁵ Hz
2. 16 × 10¹² Hz
3. 1.6 × 10¹² Hz
4. 1.6 × 10¹⁵ Hz

Question 15:

A current of 200 µA deflects the coil of a moving coil galvanometer through 60°. The current to cause deflection through π/10 radians is:

1. 30 µA
2. 120 µA
3. 60 µA
4. 180 µA

Question 16:

The atomic mass of 6C¹² is 12.000000 u and that of 6C¹³ is 13.003354 u. The required energy to remove a neutron from 6C¹³, if the mass of the neutron is 1.008665 u, will be:

1. 62.5 MeV
2. 6.25 MeV
3. 4.95 MeV
4. 49.5 MeV

Question 17:

A ball suspended by a thread swings in a vertical plane so that its acceleration in the extreme and lowest position are equal. The angle (θ) of deflection in the extreme position is:

1. tan⁻¹(√2)
2. 2tan⁻¹(1/2)
3. tan⁻¹(1/2)
4. 2tan⁻¹(1/√5)

Question 18:

Three voltmeters are joined as shown. When a potential difference is applied across A and B, their readings are V₁, V₂, and V₃. Choose the correct option.

1. V₁ = V₂
2. V₁ = V₃ − V₂
3. V₁ + V₂ > V₃
4. V₁ + V₂ = V₃

Question 19:

The total kinetic energy of 1 mole of oxygen at 27°C is:

1. 6845.5 J
2. 5942.0 J
3. 6232.5 J
4. 5670.5 J

Question 20:

The primary side of a transformer is connected to 230 V, 50 Hz supply with a turns ratio of 10:1. Load resistance is 46 Ω. The power consumed is:

1. 12.5 W
2. 10 W
3. 11.5 W
4. 12 W

Question 21:

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii R1 = 2 m and R2 = 4 m carrying current I = 4 A as per figure given below is α×10⁻⁷ T. The value of α is:

Question 22:

Two charges of −4µC and +4µC are placed at the points A(1, 0, 4)m and B(2, −1, 5)m in an electric field E = 0.20 i V/cm. The magnitude of the torque acting on the dipole is 8√α×10⁻⁵ Nm, where α = :

Question 23:

A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is:

Question 24:

A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is:

Question 25:

The reading of a pressure meter attached with a closed pipe is 4.5×10⁴ N/m². On opening the valve, water starts flowing and the reading of pressure meter falls to 2.0×10⁴ N/m². The velocity of water is found to be √V m/s. The value of V is:

Question 26:

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is:

Question 27:

A parallel beam of monochromatic light of wavelength 5000 Å is incident normally on a single narrow slit of width 0.001 mm. The light is focused by a convex lens on a screen placed on its focal plane. The first minima will be formed for the angle of diffraction of:

Question 28:

The electric potential at the surface of an atomic nucleus (Z = 50) of radius 9×10⁻¹³ cm is ×10⁶ V:

Question 29:

If Rydberg’s constant is R, the longest wavelength of radiation in Paschen series will be α×7R, where α = :

Question 30:

A series LCR circuit with L = 100π mH, C = 10⁻³ F, and R = 10 Ω is connected across an ac source of 220 V, 50 Hz supply. The power factor of the circuit would be: