$A$ message signal of frequency $8 \text{ kHz}$ and peak voltage $12 \text{ V}$ is used to modulate a carrier of frequency $1.2 \text{ MHz}$ and peak voltage $20 \text{ V}$. The modulation index is

$A$ carrier signal $C(t)=25 \sin(2.512 \times 10^{10} t)$ is amplitude modulated by a message signal $m(t)=5 \sin(1.57 \times 10^{8} t)$ and transmitted through an antenna. What will be the bandwidth of the modulated signal?

For transmitting a signal of frequency $1 \text{ kHz}$,the wavelength of the wave should be:

$A$ carrier signal $60 \sin(2\pi \times 10^6 t)$ is used to modulate an audio signal $15 \sin(300 \pi t)$. The depth of modulation is .......... $\%$.

The height of a $T.V.$ tower is $75 \ m$. What is the maximum distance in $km$ up to which $T.V.$ transmission can be received (in $.98$)? (Radius of the Earth $= 6.4 \times 10^6 \ m$).

$A$ $TV$ tower has a height of $150 \ m$. If the population density around the $TV$ tower is $10^3 \ km^{-2}$, then the population covered by the tower is (Radius of the earth, $R = 6.4 \times 10^6 \ m$). (in $\text{lakh}$)