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Question 1:

The kinetic energy of an electron, an α-particle, and a proton are given as 4K, 2K, and K respectively. The de-Broglie wavelength associated with electron (λ_e), α-particle (λ_α), and the proton (λ_p) are as follows:

1. λ_α > λ_p > λ_e
2. λ_α = λ_p > λ_e
3. λ_α = λ_p < λ_e
4. λ_α < λ_p < λ_e

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Question 2:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Earth has atmosphere whereas moon doesn’t have any atmosphere.
Reason R: The escape velocity on the moon is very small as compared to that on Earth.

Choose the correct answer from the options given below:

1. Both A and R are correct and R is the correct explanation of A
2. A is false but R is true
3. Both A and R are correct but R is NOT the correct explanation of A
4. A is true but R is false

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Question 3:

A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W, the rate at which internal energy of the system increases is:

1. 500 W
2. 600 W
3. 800 W
4. 1200 W

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Question 4:

A small ball of mass M and density ρ is dropped in a viscous liquid of density ρ_o. After some time, the ball falls with a constant velocity. What is the viscous force on the ball?

1. F = Mg(1 + ρ_o/ρ)
2. F = Mg(1 + ρ/ρ_o)
3. F = Mg(1 − ρ_o/ρ)
4. F = Mg(1 + ρρ_o)

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Question 5:

A small block of mass 100 g is tied to a spring of spring constant 7.5 N/m and length 20 cm. The other end of the spring is fixed at a point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5 rad/s about point A, the tension in the spring is:

1. 0.75 N
2. 1.5 N
3. 0.25 N
4. 0.50 N

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Question 6:

A particle is moving with constant speed in a circular path. When the particle turns by an angle of 90°, the ratio of instantaneous velocity to its average velocity is π:x√2. The value of x will be:

1. 7
2. 2
3. 1
4. 5

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Question 7:

Two resistances are given as R₁ = (10 ± 0.5)Ω and R₂ = (15 ± 0.5)Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is:

1. 2.33%
2. 4.33%
3. 5.33%
4. 6.33%

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Question 8:

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the center of the shell can be graphically represented as:

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Question 9:

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across the cross-section. The magnetic field is:

1. Zero in the region r < a and inversely proportional to r in the region r > a
2. Inversely proportional to r in the region r < a and uniform throughout in the region r > a
3. Directly proportional to r in the region r < a and inversely proportional to r in the region r > a
4. Uniform in the region r < a and inversely proportional to r in the region r > a

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Question 10:

By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 21%?

1. 12%
2. 15%
3. 14%
4. 10%

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Question 11:

The number of air molecules per cm³ increased from 3×10¹⁹ to 12×10¹⁹. The ratio of collision frequency of air molecules before and after the increase is:

1. 0.25
2. 0.75
3. 1.25
4. 0.50

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Question 12:

The energy levels of a hydrogen atom are shown. The transition corresponding to emission of the shortest wavelength is:

1. A
2. D
3. C
4. B

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Question 13:

For the plane electromagnetic wave given by E = E₀ sin(ωt - kx) and B = B₀ sin(ωt - kx), the ratio of average electric energy density to average magnetic energy density is:

1. 2
2. 1/2
3. 1
4. 4

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Question 14:

A planet has double the mass of the Earth. Its average density is equal to that of the Earth. An object weighing W on Earth will weigh on that planet:

1. 2^1/3W
2. 2W
3. W
4. 2^2/3W

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Question 15:

The resistivity (ρ) of a semiconductor varies with temperature. Which of the following curves represents the correct behavior?

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Question 16:

A monochromatic light wave with wavelength λ₁ and frequency ν₁ in air enters another medium. If the angle of incidence and angle of refraction at the interface are 45° and 30° respectively, then the wavelength λ₂ and frequency ν₂ of the refracted wave are:

1. λ₂ = (1/√2) λ₁, ν₂ = ν₁
2. λ₂ = λ₁, ν₂ = (1/√2) ν₁
3. λ₂ = λ₁, ν₂ = √2 ν₁
4. λ₂ = √2 λ₁, ν₂ = ν₁

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Question 17:

A mass m is attached to two springs of spring constants K₁ and K₂, respectively, as shown. The time period of oscillation of the mass m on a frictionless surface is:

1. (1/2π) √(m/(K₁ − K₂))
2. (1/2π) √((K₁ + K₂)/m)
3. 2π √(m/(K₁ + K₂))
4. 2π √((K₁ − K₂)/m)

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Question 18:

Identify the logic gate that is equivalent to the given circuit diagram.

1. NOR
2. OR
3. NAND
4. AND

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Question 19:

Which of the following scenarios will result in an induced emf in a coil?

1. A and B only
2. C and D only
3. B and C only
4. A and C only

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Question 20:

Given below are two statements: Assertion (A) and Reason (R).
Assertion A: When a body is projected at an angle of 45°, its range is maximum.
Reason R: For maximum range, the value of sin 2θ should be equal to 1.

1. Both A and R are correct but R is NOT the correct explanation of A
2. A is false but R is true
3. Both A and R are correct and R is the correct explanation of A
4. A is true but R is false

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Question 21:

Two identical circular wires of radius 20 cm and carrying current √2 A are placed in perpendicular planes as shown in the figure. The net magnetic field at the center of the circular wires is × 10^-8 T.

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Question 22:

A steel rod has a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN stretches it along its length. Young’s modulus of steel is 2.0 × 10¹¹ N/m². The longitudinal strain produced in the wire is × 10^-5.

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Question 23:

The length of a metallic wire is increased by 20% and its area of cross-section is reduced by 4%. The percentage change in resistance of the metallic wire is:

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Question 24:

The radius of the fifth orbit of Li⁺⁺ is × 10^-12 m. Take the radius of hydrogen atom = 0.51 Å.

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Question 25:

A particle of mass 10 g moves in a straight line with retardation 2x, where x is the displacement in SI units. Its loss of kinetic energy for the above displacement is (10/x)^-n J. The value of n will be:

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Question 26:

An ideal transformer with a purely resistive load operates at 12 kV on the primary side. It supplies electrical energy to a number of nearby houses at 120 V. The average rate of energy consumption in the houses served by the transformer is 60 kW. The value of resistive load (R_s) required in the secondary circuit will be in mΩ:

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Question 27:

A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant K = 4. The thickness of the dielectric material is x, where x < d. Let C₁ and C₂ be the capacitance of the system for x = 1/3d and x = 2/3d, respectively. If C₁ = 2 µF, the value of C₂ is in µF:

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Question 28:

Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centers of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is × 10^-3 kg·m²:

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Question 29:

A person driving a car at a constant speed of 15 m/s is approaching a vertical wall. The person notices a change of 40 Hz in the frequency of his car's horn upon reflection from the wall. The frequency of the horn is in Hz:

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Question 30:

A pole is vertically submerged in a swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of 30° with the surface of water. If the swimming pool is filled to a height of 1.5 m, then the height of the pole above the water surface in centimeters is (n_w = 4/3):

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