$A$ carrier wave of peak voltage $12 \, V$ is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of $75 \%$? ...... $V$

$A$ carrier wave of peak voltage $20 V$ is used to transmit a message signal. For getting a modulation index of $60 \%$, the peak voltage of the modulating signal is (in $V$)

The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance $49\,\mu H$ and a capacitance of $2.5\,nF$. It is modulated by an audio signal of $12\,kHz$. The frequency range occupied by the side bands is

The height of the transmitting antenna, if $TV$ programs have to cover a population in an area of radius $64 \ km$, is: [Use Radius of earth $= 6.4 \times 10^6 \ m$] (in $m$)

$A$ carrier is simultaneously modulated by two sine waves with modulation indices of $0.3$ and $0.4$; then the total modulation index is

Given the electric field of a complete amplitude modulated wave as $\vec E = \hat i E_c (1 + \frac{E_m}{E_c} \cos \omega_m t) \cos \omega_c t$,where the subscript $c$ stands for the carrier wave and $m$ for the modulating signal. The frequencies present in the modulated wave are: