Correct Answer: B

Step-by-step Solution: According to the law of equipartition of energy, each degree of freedom has an average energy of ½ kT. A monatomic gas molecule has 3 degrees of freedom, so its average kinetic energy is (3/2) kT.

Correct Answer: B

Step-by-step Solution: When a light source moves away from the observer, the observed wavelength increases (frequency decreases), shifting towards the red end of the spectrum. This is called redshift.

Correct Answer: A

Step-by-step Solution: Resolving power = D / (1.22 λ). It can be increased by increasing the aperture (diameter D) of the objective lens or by using light of shorter wavelength.

Correct Answer: B

Step-by-step Solution: λ = h / p = h / √(2mE). Since average energy E ∝ T, then λ ∝ 1 / √T.

Correct Answer: A

Step-by-step Solution: T_half = ln 2 / λ and τ = 1 / λ. Thus T_half = (ln 2) * τ ≈ 0.693 τ.

Correct Answer: B

Step-by-step Solution: In a full-wave rectifier, both halves of the AC cycle are rectified, so the ripple frequency is twice the input frequency. 2 * 50 = 100 Hz.

Correct Answer: C

Step-by-step Solution: The truth table for XOR shows that the output is 1 when one input is 1 and the other is 0. If both are the same (both 0 or both 1), the output is 0.

Correct Answer: A

Step-by-step Solution: Sky waves (ionospheric reflection) are effective for frequencies between roughly 2 MHz and 30 MHz. Frequencies above 30 MHz usually penetrate the ionosphere.

Correct Answer: B

Step-by-step Solution: K = ½ k(A² - x²) and U = ½ kx². Setting K = U gives A² - x² = x² => 2x² = A² => x = A / √2.

Correct Answer: D

Step-by-step Solution: According to the Stefan-Boltzmann Law, the power radiated by a black body is P = σAT⁴. Thus, the power is proportional to the fourth power of the absolute temperature.