If the highest frequency modulating a carrier is $5\, kHz$,then the number of $AM$ broadcast stations accommodated in a $90\, kHz$ bandwidth are ....... .

$A$ transmitting antenna has a height of $320\, m$ and that of the receiving antenna is $2000\, m$. The maximum distance between them for satisfactory communication in line-of-sight mode is $d$. The value of $d$ is $\ldots \ldots \, km$.

$A$ transmitting antenna has a height of $20 \,m$. What will be the height of the receiving antenna if the maximum distance between them for satisfactory communication in line-of-sight $(LOS)$ mode is $40 \,km$ (in $\,m$)? (The radius of the Earth is $6400 \,km$.)

The modulation index used in amplitude modulation of a message signal of peak voltage $10 \,V$ is $0.5$. By how much should the peak voltage of the carrier signal be changed, so as to obtain the modulation index of $0.8$, keeping the peak voltage of the message signal the same as before?

Find the modulation index of an $AM$ wave having $8\,V$ variation where maximum amplitude of the $AM$ wave is $9\,V$.

$A$ $TV$ 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: