The mathematical form of an $AM$ wave is given by $e = 50 (1 + 0.5 \sin(2\pi \times 5 \times 10^{3} t)) \sin(31.4 \times 10^{6} t) \text{ V}$. The modulation index of the given $AM$ wave is .......

$A$ telephonic communication service is working at a carrier frequency of $10 \ GHz$. Only $10\%$ of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of $5 \ kHz$?

In frequency modulation,........

$A$ carrier wave $60 \sin(2\pi \times 10^6 t)$ is modulated by a signal $15 \sin(300\pi t)$. The modulation index is: (in $\%$)

Three signals related to amplitude modulation are shown in the figure. The correct assignment of the signals is

The size of the antenna required for a carrier wave of frequency $3 \text{ MHz}$ is: (in $\text{ m}$)