Question 2:

In a cuboid of dimensions 2L × 2L × L, a charge q is placed at the center of the surface S having area 4L². The flux through the opposite surface to S is:

1. q / 12ε₀
2. q / 3ε₀
3. q / 2ε₀
4. q / 6ε₀

Question 3:

Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is:

1. 3:1
2. 1:1
3. 1:3
4. 1:27

Question 4:

A single current-carrying loop of wire carrying current I flows in the anticlockwise direction (seen from the +z direction) and lies in the xy plane. The plot of the ĵ component of magnetic field (By) at a distance a (less than the radius of the coil) and on the yz plane vs z coordinate looks like:

1. (Not shown)
2. (Not shown)
3. (Correct graph)
4. (Not shown)

Question 5:

The magnitude of magnetic induction at the mid-point O due to the current arrangement shown in the figure is:

1. μ₀I / (2πa)
2. 0
3. μ₀I / (4πa)
4. μ₀I / (πa)

Question 6:

Find the mutual inductance in the arrangement, when a small circular loop of radius R is placed inside a large square loop of side L (L ≫ R). The loops are coplanar and their centers coincide:

1. M = √2μ₀R² / L
2. M = 2√2μ₀R / L²
3. M = 2√2μ₀R² / L
4. M = √2μ₀R / L²

Question 6:

Find the mutual inductance in the arrangement, when a small circular loop of radius R is placed inside a large square loop of side L (L ≫ R). The loops are coplanar and their centers coincide:

1. M = √2μ₀R² / L
2. M = 2√2μ₀R / L²
3. M = 2√2μ₀R² / L
4. M = √2μ₀R / L²

Question 7:

Which of the following are true?

A. Speed of light in vacuum depends on the direction of propagation.

B. Speed of light in a medium is independent of the wavelength of light.

C. Speed of light is independent of the motion of the source.

D. Speed of light in a medium is independent of intensity.

Choose the correct answer from the options given below:

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

Question 8:

In a Young’s double slit experiment, two slits are illuminated with light of wavelength 800 nm. The first minimum is detected at P. The value of slit separation a is:

1. 0.4 mm
2. 0.5 mm
3. 0.2 mm
4. 0.1 mm

Question 9:

A stone is projected at an angle of 30° to the horizontal. The ratio of kinetic energy at projection to its kinetic energy at the highest point is:

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

Question 10:

A block of mass m slides down a plane inclined at an angle of 30° with an acceleration of g/4. The coefficient of kinetic friction is:

1. (2√3 + 1) / 2
2. 1 / 2√3
3. √3 / 2
4. (2√3 − 1) / 2

Question 11:

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of the car will be, if the friction coefficient between tyres and road is 0.34. (Take g = 10 m/s²):

1. 13.4 m/s
2. 22.4 m/s
3. 13 m/s
4. 17 m/s

Question 12:

Two particles of equal mass m move in a circle of radius r under the action of their mutual gravitational attraction. The speed of each particle will be:

1. √(GM / 2r)
2. √(4GM / r)
3. √(GM / r)
4. √(GM / 4r)

Question 13:

The surface tension of a soap bubble is 2 × 10⁻² N/m. Work done to increase the radius of the bubble from 3.5 cm to 7 cm will be:

1. 4.072 × 10⁻³ J
2. 5.76 × 10⁻³ J
3. 1.848 × 10⁻³ J
4. 9.24 × 10⁻³ J

Question 14:

Assertion A: If dQ and dW represent the heat supplied to the system and the work done on the system respectively, then according to the first law of thermodynamics dQ = dU − dW.
Reason R: First law of thermodynamics is based on the law of conservation of energy.

In the light of the above statements, choose the correct answer from the options given below:

1. A is correct but R is not correct
2. A is not correct but R is correct
3. Both A and R are correct, and R is the correct explanation of A
4. Both A and R are correct, but R is not the correct explanation of A

Question 15:

A bicycle tyre is filled with air at a pressure of 270 kPa at 27°C. The approximate pressure of the air in the tyre when the temperature increases to 36°C is:

1. 270 kPa
2. 262 kPa
3. 278 kPa
4. 360 kPa

Question 16:

A person observes two moving trains, A reaching the station and B leaving the station with equal speed of 30 m/s. If both trains emit sounds with frequency 300 Hz, the approximate difference of frequencies heard by the person will be:

1. 33 Hz
2. 55 Hz
3. 80 Hz
4. 10 Hz

Question 17:

If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be:

1. 32 km
2. 28 km
3. 36 km
4. 64 km

Question 18:

The threshold wavelength for photoelectric emission from a material is 5500 Å. Photoelectrons will be emitted when this material is illuminated with monochromatic radiation from:

• A. 75 W infra-red lamp
• B. 10 W infra-red lamp
• C. 75 W ultra-violet lamp
• D. 10 W ultra-violet lamp

Choose the correct answer from the options given below:

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

Question 19:

If a radioactive element with a half-life of 30 min undergoes beta decay, the fraction of the radioactive element that remains undecayed after 90 min is:

1. 1/8
2. 1/16
3. 1/4
4. 1/2

Question 20:

Which of the following statements is not correct in the case of light emitting diodes (LEDs)?

• A. It is a heavily doped p-n junction.
• B. It emits light only when it is forward biased.
• C. It emits light only when it is reverse biased.
• D. The energy of the light emitted is equal to or slightly less than the energy gap of the semiconductor used.

Choose the correct answer from the options given below:

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

Question 21:

A radioactive element ²⁴²₉₂X emits two α-particles, one electron, and two positrons. The product nucleus is represented by ²³⁴_PY. The value of P is ——.

Question 22:

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is —– degrees.