Identify the mathematical expression for amplitude modulated wave:

The correct answer is Option (3) → \( \left\{A_{C}+K_2 v_{m}(t)\right\}\sin\left(\omega_{C}t+\phi\right) \)

In amplitude modulation only the amplitude of the carrier \( A_C\sin(\omega_C t+\phi) \) is made to follow the message signal \( v_m(t) \); its frequency \( \omega_C \) and phase \( \phi \) stay fixed. So the amplitude \( A_C \) is replaced by \( A_C + K_2 v_m(t) \), which gives Option (3).

Why the other options are incorrect

• Option (1) — Incorrect. Here the message changes the frequency \( \omega_C \) of the carrier, which is frequency modulation.

• Option (2) — Incorrect. Here the message changes the phase of the carrier, which is phase modulation.

• Option (4) — Incorrect. The amplitude is only the product \( A_C v_m(t) \) and the carrier term \( A_C \) alone is missing, so the carrier amplitude is not retained as the base value that the signal adds to.

Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.

NCERT (Pre-rationalised edition, 2022-23):
Amplitude Modulation – “In amplitude modulation the amplitude of the carrier is varied in accordance with the information signal. … The modulated signal c_m (t) can be written as

    \( \displaystyle c_m(t) = (A_c + A_m \sin\omega_m t)\sin\omega_c t \)”