$A$ 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?

Carrier waves are used for communicating signals over long distances because:

For a coaxial cable,the typical repeater spacing is approximately............$km$.

Given below are two statements:
Statement-$I$: $A$ speech signal of $2 \, kHz$ is used to modulate a carrier signal of $1 \, MHz$. The bandwidth requirement for the signal is $4 \, kHz$.
Statement-$II$: The sideband frequencies are $1002 \, kHz$ and $998 \, kHz$.
In the light of the above statements,choose the correct answer from the options given below:

$A$ $T$.$V$. tower has a height of $100 \, m$. The average population density around the tower is $1000 \, km^{-2}$ and the radius of the earth is $6.37 \times 10^6 \, m$. The population covered is

If the maximum and minimum voltage of an amplitude modulated wave are $V_{max}$ and $V_{min}$ respectively,then the modulation factor is: