$A$ carrier wave of peak voltage $15 V$ is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of $80\%$ (in $V$)?

Given below in the left column are different modes of communication using the kinds of waves given in the right column.

$A$. Optical Fiber Communication	$P$. Ultrasound
$B$. Radar	$Q$. Infrared Light
$C$. Sonar	$R$. Microwaves
$D$. Mobile Phones	$S$. Radio Waves

From the options given below, find the most appropriate match between entries in the left and the right column.

$A$ 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 $\,m$)

The height of the transmitting antenna, if $TV$ programs have to cover a population in an area of radius $64 \ km$, is: [Use Radius of earth $= 6.4 \times 10^6 \ m$] (in $m$)

$A$ $100\, V$ carrier wave is made to vary between $160\, V$ and $40\, V$ by a modulating signal. What is the modulation index?

For transmitting a signal of frequency $1000 \text{ kHz}$, the minimum length of the antenna is (in $\text{ m}$)