Question

an audio signal of amplitude one fourth the ampltude of carrier wave is used in amplitude modulation what is modulation index

Answer 1

Modulation index m can be given as the ratio of amplitude of the modulating wave A_M to amplitude of the carrier wave A_C.
$m=\frac{A_M}{A_C}$
As given A_M is one fourth of A_C,

A_M = 1/4 A_C
Therefore
$$\begin{gathered} m=\frac{A_M}{4A_M} \\ m=\frac{1}{4} \\ m=0.25 \end{gathered}$$