$A$ transmitting antenna has a height of $320\, m$ and that of the receiving antenna is $2000\, m$. The maximum distance between them for satisfactory communication in line-of-sight mode is $d$. The value of $d$ is $\ldots \ldots \, km$.

An audio signal consists of two distinct sounds: one is a human speech signal in the frequency band of $200\,Hz$ to $2700\,Hz,$ while the other is a high-frequency music signal in the frequency band of $10200\,Hz$ to $15200\,Hz.$ The ratio of the $AM$ signal bandwidth required to send both the signals together to the $AM$ signal bandwidth required to send just the human speech is

Two identical antennas mounted on identical towers are separated from each other by a distance of $45 \, km$. What should be the minimum height of the receiving antenna to receive the signals in line of sight? (Assume radius of earth is $6400 \, km$)

$A$ message signal of frequency $f_m$ is used to modulate a carrier of frequency $f_c$. If the sidebands are $f_1$ and $f_2$, then the ratio $\frac{f_c}{f_m}$ is:

Match List $I$ with List $II$ :

List $I$	List $II$
$A$. Attenuation	$I$. Combination of a receiver and transmitter.
$B$. Transducer	$II$. Process of retrieval of information from the carrier wave at receiver.
$C$. Demodulation	$III$. Converts one form of energy into another.
$D$. Repeater	$IV$. Loss of strength of a signal while propagating through a medium.

Choose the correct answer from the options given below:

The minimum size of an antenna for transmitting electromagnetic waves at $1500 \text{ MHz}$ is