In $AM$ modulation,a signal is modulated on a carrier wave such that maximum and minimum amplitude are found to be $6\,V$ and $2\,V$ respectively. The modulation index is $\dots \%$.

The heights of the transmitting and receiving antennas are $33.8 \ m$ and $64.8 \ m$ respectively. The maximum distance between the antennas for satisfactory communication in a line of sight mode is (Radius of the earth $= 6400 \ km$) (in $km$)

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 $m$)

Amplitude modulation has

$A$ bandwidth of $6 \, \text{MHz}$ is available for $A.M.$ transmission. If the maximum audio signal frequency used for modulating the carrier wave is not to exceed $6 \, \text{kHz}$,the number of stations that can be broadcasted within this band simultaneously without interfering with each other will be ..... .

$A$ modulated signal $C_m(t)$ has the form $C_m(t) = 30 \sin(300\pi t) + 10 \cos(200\pi t) - 10 \cos(400\pi t)$. The carrier frequency $f_c$,the modulating frequency $f_m$,and the modulation index $\mu$ are respectively given by: