If a transmitting antenna of height $105 \,m$ is placed on a hill, then its coverage area is (in $\,km^2$)

Assertion $(A)$: Television signals are received through sky-wave propagation.
Reason $(R)$: The ionosphere reflects electromagnetic waves of frequencies in the range $(3-30)$ $MHz$.
Choose the correct option.

For effective transmission of a wave with frequency $3000 \text{ kHz}$,the minimum length of the antenna should be ...... $m$.

An $FM$ broadcast transmitter,using a modulating signal of frequency $20\,kHz$,has a deviation ratio of $10$. The bandwidth required for transmission is $.......kHz$.

$A$ carrier wave has a frequency of $1000 \, kHz$ and an amplitude of $20 \, V$. It is amplitude modulated by a signal wave of frequency $10 \, kHz$ and amplitude $10 \, V$. The modulation index and the frequencies of the $LSB$ and $USB$ are,respectively:

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