CUET · PHYSICS · PYQ PAPER 2023

A message signal of frequency \(\omega_m\) is superposed on a carrier wave of frequency \(\omega_c\) to get an amplitude modulated wave (AM). The frequency of the AM wave will be :

A \(\omega_m\)
B \(\omega_c\)
C \(\frac{\omega_c+\omega_m}{2}\)
D \(\frac{\omega_c-\omega_m}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\omega_c\)

Step-by-step Solution

Detailed explanation

In amplitude modulation, the message signal only modifies the amplitude of the carrier wave, while the frequency of the oscillation itself remains that of the carrier wave ( \(\omega_c\) ). While the process creates sidebands at \(\omega_c \pm \omega_m\), the fundamental…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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List-I	List-II
(A) k	(I) \(\frac{2}{15}\)
(B) \(P ( x =1)\)	(II) \(\frac{1}{5}\)
(C) \(P (1<x<3)\)	(III) \(\frac{8}{15}\)
(D) \(P(x \geq 2)\)	(IV) \(\frac{4}{15}\)