$A$ transmitting antenna at the top of a tower has a height of $50\, m$ and the height of the receiving antenna is $80\, m$. What is the range of communication for Line of Sight (LoS) mode? (In $km$)
[Use radius of earth $R = 6400\, km$]

The mathematical form of an $AM$ wave is given by $e = 50 (1 + 0.5 \sin(2\pi \times 5 \times 10^{3} t)) \sin(31.4 \times 10^{6} t) \text{ volts}$. Which of the following frequencies is absent in the given $AM$ wave?

Match Column $A$ (layers in the ionosphere for skywave propagation) with Column $B$ (their height range).

Column $A$	Column $B$
$A$. $D$-layer	$I$. $250-400 \ km$
$B$. $E$-layer	$II$. $170-190 \ km$
$C$. $F_1$-layer	$III$. $95-120 \ km$
$D$. $F_2$-layer	$IV$. $65-75 \ km$

In an $AM$ wave,the frequencies of $LSB$ and $USB$ are $2.99 \ MHz$ and $3.01 \ MHz$ respectively. The carrier frequency is ....... and the modulating frequency is .......

$A$ ground receiver station is receiving a signal at $5\, MHz$ transmitted from a ground transmitter at a height of $300\, m$,located at a distance of $100\, km$ from the receiver station. Given: Radius of Earth $R = 6.4 \times 10^6\, m$,$N_{\max}$ of ionosphere = $10^{12}\, m^{-3}$. Identify the mode of propagation.

$A$ transmitting antenna of height $20 \,m$ and a receiving antenna of height $h$ are separated by a distance of $40 \,km$ for satisfactory communication in line-of-sight $(LOS)$ mode. The value of $h$ is (Given: radius of Earth is $6400 \,km$). (in $\,m$)