Which of the following statements are correct?

(A) According to wave theory, energy carried by a wave depends on the amplitude of the wave, not on the speed of wave propagation
(B) For a given frequency, intensity of light in the photon picture is determined by the number of photons crossing a unit area
(C) At a large distance from the source, a small portion of the spherical wave can be approximated by a plane wave
(D) the reflected and refracted light both have different frequencies than the incident frequency

Choose the correct answer from the options given below:

(A) and (C) only

The correct answer is Option (2) → (A) and (C) only

Note: The given answer is as per NTA answer Key. However, the correct statements should be A, B and C only as explained below:

(A) According to wave theory, energy carried by a wave depends on the amplitude of the wave, not on the speed of wave propagation. Correct. In wave theory, the energy (and intensity) carried by a wave is proportional to the square of its amplitude ($I \propto A^2$). It does not depend on the speed of propagation.
(B) For a given frequency, intensity of light in the photon picture is determined by the number of photons crossing a unit area. Correct. In the photon picture (quantum theory), the intensity of light for a monochromatic beam (given frequency) is defined by the flux of photons. Specifically, $I = nh\nu$, where $n$ is the number of photons crossing a unit area per unit time. (As per NTA this statement is incorrect).
(C) At a large distance from the source, a small portion of the spherical wave can be approximated by a plane wave.  Correct. As a spherical wavefront travels away from a point source, its radius of curvature increases. At a very large distance, the curvature becomes negligible, and a small portion of that wavefront can be treated as a plane wave.
(D) the reflected and refracted light both have different frequencies than the incident frequency. Incorrect.When light is reflected or refracted, the frequency remains constant because it is determined by the source of the light. While the speed and wavelength change during refraction, the frequency does not change as the wave passes from one medium to another.