In an amplitude modulator circuit, the carrier wave is given by, C(t)=4sin(2000πt) while modulating signal is given by, m(t)=2sin(200πt). The values of modulation index and lower side band frequency are:

Correct option is A. 0.5 and 9kHz
Modulation index is given by
m = Am/Ac = 2/4 = 0.5
(a) carrier wave frequency is given by = 2πfc = 2 x 10^4
fc = 10kHz
(b) modulation wave frequency(fm) 2πfm = 200π => fm = 1kHz
lower side band frequency => fc - f => 10kHz - 1kHz = 9kHz