In a communication system,a repeater is used to extend the range of transmission. It is a combination of:

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:

$A$ $TV$ tower has a height of $100 \ m$. The average population density around the tower is $1000 \ \text{per} \ km^2$. The radius of the earth is $6.4 \times 10^6 \ m$. The population covered by the tower is:

$A$ 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 $V$)

In the process of space communication,the use of a modem is necessary. In which one of the following modes does a modem act as a modulator and a demodulator respectively?

If the height of the transmitting tower is increased by $30 \%$,then the area covered by it increases by (in $\%$)