$A$ message signal of frequency $14 kHz$ is used to modulate a carrier of frequency $900 kHz$. The frequencies of the sidebands are:

If a $TV$ transmission antenna covers a radius of $128 \, km$,what should be the height of the antenna in $m$?

$A$ message signal of frequency $15 kHz$ is used to modulate a carrier of frequency $v_c$. If the side bands produced are $1515 kHz$ and $1485 kHz$,then $v_c$ is (in $MHz$)

Given the electric field of a complete amplitude modulated wave as $\vec E = \hat i E_c (1 + \frac{E_m}{E_c} \cos \omega_m t) \cos \omega_c t$,where the subscript $c$ stands for the carrier wave and $m$ for the modulating signal. The frequencies present in the modulated wave are:

If the area covered by an $FM$ radio station is to be doubled,by what factor must the height of the antenna be increased?

We do not transmit low frequency signals to long distances because:
$(a)$ The size of the antenna should be comparable to signal wavelength,which is impractical for a signal of longer wavelength.
$(b)$ Effective power radiated by a long wavelength baseband signal would be high.
$(c)$ We want to avoid mixing up signals transmitted by different transmitters simultaneously.
$(d)$ Low frequency signals can be sent to long distances by superimposing them with a high frequency wave.
Therefore,the most suitable options are: