Peak voltage of a modulating signal is 2 V. The carrier wave is represented by C(t) = 4 sin(8π t) V. The modulation index of modulated signal is:

0.5

Modulation index is a measure of extent of modulation done on a carrier signal. In Amplitude modulation, it is defined as the ratio of the amplitude of modulating signal to that of the carrier signal.

$ \mu = \frac{A_m}{A_c} = \frac{2}{4} = 0.5$