For $100\%$ modulation $(AM)$,the useful part of the total power radiated is

$A$ message signal of frequency $5\,kHz$ is used to modulate a carrier signal of frequency $2\,MHz$. The bandwidth for amplitude modulation is $..........\,kHz$.

Given below are two statements
Statement $I:$ For transmitting a signal,the size of the antenna $(l)$ should be comparable to the wavelength of the signal (at least $l = \frac{\lambda}{4}$ in dimension).
Statement $II:$ In amplitude modulation,the amplitude of the carrier wave remains constant (unchanged).
In the light of the above statements,choose the most appropriate answer from the options given below.

The height of a transmission antenna is $49 \,m$ and that of the receiving antenna is $64 \,m$. What should be the maximum distance between them for line of sight transmission (in $\,km$)?

$A$ $TV$ transmitting antenna is $128 \ m$ tall. If the receiving antenna is at the ground level,the maximum distance between them for satisfactory communication in line-of-sight mode is (radius of the earth $R_e = 6.4 \times 10^6 \ m$):

In short wave communication, waves of which of the following frequencies will be reflected back by the ionospheric layer having an electron density of $10^{11} \text{ per } m^3$ (in $\text{ MHz}$)?