What is the minimum height of an antenna required to transmit a radio signal of frequency $20 \text{ MHz}$?

$A$ signal of frequency $10 kHz$ and peak voltage $10 V$ is used to amplitude modulate a carrier of frequency $1 MHz$ and peak voltage $20 V$. The side-band frequencies in $kHz$ are

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

The radio horizon of the transmission of an antenna placed on the $20^{\text{th}}$ floor in a shopping mall,where the height of each floor is $2 \,m$,is (Radius of Earth is $6.4 \times 10^6 \,m$): (in $\,km$)

$A$ transmitting and receiving antenna have a height of $d$ meters each. The maximum distance between them for satisfactory communication in Line-of-Sight $(LOS)$ mode is $2d$ kilometers. If the radius of the Earth is $6400 \text{ km}$, then the value of $d$ is: (in $\text{ m}$)

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