Correct Answer - Option 3 : cos (200 πt)
x(t) = sin 200 πt + 2 sin (400 πt)
g(t) = x(t) sin 400 πt
g(t) = [sin 200 πt + 2 sin 400 πt] sin 400 πt
\(= 12\;\left[ {\cos 200\;\pi t - \cos 600\pi t} \right] + \cos 0\pi t - \cos 800\pi t\)
Now, this signal is passed through LPF having a cut-off frequency of 400 π Hz and passband gain of 2.
So output signal = cos 200 πt.
Option 3 is correct.