Question 1:

A proton, an electron, and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as:

1. λe > λα > λp
2. λα < λp < λe
3. λp < λe < λα
4. λp > λe > λα

Question 2:

A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s, respectively. The average speed of the particle during the motion is:

1. 8.8 m/s
2. 10 m/s
3. 9.2 m/s
4. 8 m/s

Question 3:

A plane EM wave is propagating along the x-direction. It has a wavelength of 4 mm. If the electric field is in the y-direction with the maximum magnitude of 60 V/m, the equation for the magnetic field is:

1. Bz = 60 sin[π/2(x − 3 × 10⁸t)] k̂ T
2. Bz = 2 × 10⁻⁷ sin[π/2 × 10³(x − 3 × 10⁸t)] k̂ T
3. Bx = 60 sin[π/2(x − 3 × 10⁸t)] î T
4. Bz = 2 × 10⁻⁷ sin[π/2(x − 3 × 10⁸t)] k̂ T

Question 4:

Given below are two statements:

Statement (I): When currents vary with time, Newton’s third law is valid only if momentum carried by the electromagnetic field is taken into account.
Statement (II): Ampere’s circuital law does not depend on Biot-Savart’s law.

Choose the correct answer:

1. Both Statement I and Statement II are false.
2. Statement I is true but Statement II is false.
3. Statement I is false but Statement II is true.
4. Both Statement I and Statement II are true.

Question 5:

A light-emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is 1.42 eV. The wavelength of light emitted from the LED is:

1. 650 nm
2. 1243 nm
3. 875 nm
4. 1400 nm

Question 6:

A sphere of relative density σ and diameter D has a concentric cavity of diameter d. The ratio of D/d, if it just floats on water in a tank, is:

1. (σ / (σ − 1))^(1/3)
2. ((σ + 1) / (σ − 1))^(1/3)
3. ((σ − 1) / σ)^(1/3)
4. ((σ − 2) / (σ + 2))^(1/3)

Question 7:

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is A/3 and the height is d, the capacitance of the arrangement is:

1. (11ϵ₀A) / (18d)
2. (13ϵ₀A) / (17d)
3. (11ϵ₀A) / (20d)
4. (18ϵ₀A) / (11d)

Question 8:

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

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

Question 9:

The dimensional formula of latent heat is:

1. [M₀L T⁻²]
2. [MLT⁻²]
3. [M₀L²T⁻²]
4. [ML²T²]

Question 10:

The volume of an ideal gas (γ = 1.5) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

1. 4/5
2. 16/25
3. 8/5√5
4. √2/5

Question 11:

The energy equivalent of 1 g of substance is:

1. 11.2 × 10²⁴ MeV
2. 5.6 × 10¹² MeV
3. 5.6 eV
4. 5.6 × 10⁶ MeV

Question 12:

An astronaut takes a ball of mass m from Earth to space. He throws the ball into a circular orbit about Earth at an altitude of 318.5 km. From Earth’s surface to the orbit, the change in total mechanical energy of the ball is xGMem / 21Re. The value of x is:

1. 11
2. 9
3. 12
4. 10

Question 13:

Given below are two statements:

Statement (I): When currents vary with time, Newton’s third law is valid only if momentum carried by the electromagnetic field is taken into account.
Statement (II): Ampere’s circuital law does not depend on Biot-Savart’s law.

Choose the correct answer:

1. Both Statement I and Statement II are false.
2. Statement I is true but Statement II is false.
3. Statement I is false but Statement II is true.
4. Both Statement I and Statement II are true.

Question 14:

A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v = α√x, where α is a constant. The total work done by all the forces applied on the particle during its displacement from x = 0 to x = d, will be:

1. m / 2α²d
2. md / 2α²
3. mα²d / 2
4. 2mα²d

Question 15:

A galvanometer has a coil of resistance 200Ω with a full-scale deflection at 20µA. The value of resistance to be added to use it as an ammeter of range 0−20mA is:

1. 0.40Ω
2. 0.20Ω
3. 0.50Ω
4. 0.10Ω

Question 16:

A heavy iron bar, of weight W, is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is:

1. W/2
2. W
3. W cos θ
4. W sin θ

Question 17:

One main scale division of a vernier caliper is equal to m units. If nth division of the main scale coincides with (n+1)th division of the vernier scale, the least count of the vernier caliper is:

1. n / (n+1)
2. m / (n+1)
3. 1 / (n+1)
4. m / n(n+1)

Question 18:

A bulb and a capacitor are connected in series across an AC supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:

1. increases
2. remains same
3. becomes zero
4. decreases

Question 19:

The equivalent resistance between A and B is:

1. 18Ω
2. 25Ω
3. 27Ω
4. 19Ω

Question 20:

A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If the adiabatic constant for the gas is γ = 3/2, then the work done by the gas in the process is:

1. RT [2 − √2]
2. R T [2 − √2]
3. RT [2 + √2]
4. T R [2 + √2]

Question 21:

If vec a and vec b make an angle cos⁻¹(5/9) with each other, then |vec a + vec b| = √2|vec a − vec b| for |vec a| = n|vec b|. The integer value of n is:

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

Question 22:

At the center of a half-ring of radius R = 10 cm and linear charge density 4 nC/m, the potential is xπV. The value of x is:

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

Question 23:

A star has 100% helium composition. It starts to convert three 4He into 12C via the triple alpha process as: 4He + 4He + 4He → 12C + Q. The mass of the star is 2.0 × 10³² kg and it generates energy at the rate of 5.808 × 10³⁰ W. The rate of converting these 4He to 12C is n × 10⁴² s⁻¹, where n is:

1. 10
2. 20
3. 15
4. 25

Question 24:

In a Young’s double-slit experiment, the intensity at a point is 1/4 of the maximum intensity. The minimum distance of the point from the central maximum is x μm. (Given: λ = 600 nm, d = 1.0 mm, D = 1.0 m)

1. 100
2. 200
3. 300
4. 400

Question 25:

A string is wrapped around the rim of a wheel of moment of inertia 0.40 kgm² and radius 10 cm. The wheel is free to rotate about its axis. Initially, the wheel is at rest. The string is now pulled by a force of 40N. The angular velocity of the wheel after 10 s is x rad/s, where x is:

1. 50
2. 75
3. 100
4. 150

Question 26:

A square loop of edge length 2m carrying a current of 2A is placed with its edges parallel to the x-y-axis. A magnetic field is passing through the x-y-plane and is expressed as: B = B₀(1 + 4x)k̂, where B₀ = 5T. The net magnetic force experienced by the loop is x N.

1. 120
2. 160
3. 180
4. 200

Question 27:

Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. The Young's modulus of the material of the wire is 1 × 10¹¹ N/m². The original length of the wire is 2 m, and the area of the cross-section is 2 cm². The wire will extend in length by ........ µm.

Question 28:

When a coil is connected across a 20 V DC supply, it draws a current of 5 A. When it is connected across a 20 V, 50 Hz AC supply, it draws a current of 4 A. The self-inductance of the coil is ...... mH. (π = 3)

Question 29:

The position, velocity, and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m, 2 m/s, and 16 m/s² at a certain instant. The amplitude of the motion is √x m, where x is ........

Question 30:

The current flowing through the 1 Ω resistor is n/10. The value of n is ........

Diagram: