$A$ 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 $MHz$)

Consider the following statements regarding satellite communication:
$1$. Frequencies between $1.5 \text{ MHz}$ and $1 \text{ MHz}$ are used in satellite communication.
$2$. The frequencies for uplink and downlink are different.
$3$. The orbit of a geostationary satellite makes an angle of $0^{\circ}$ with the equatorial plane of the Earth.
Which of the above statements are correct?

$A$ square wave of the modulating signal is shown in the figure. The carrier wave is given by $C(t) = 5 \sin(8\pi t) \text{ V}$. The modulation index is:

$A$ $TV$ transmission tower of height $h$ covers a range of distance $d$. By how much will the range change if the height is increased to $3/2 h$?

In an amplitude modulated wave for an audio frequency of $500 \, \text{cycles/second}$, the appropriate carrier frequency will be ........ $\text{cycles/second}$.

The mathematical form of an $AM$ wave is given by $e = 50 (1 + 0.5 \sin(2\pi \times 5 \times 10^{3} t)) \sin(31.4 \times 10^{6} t) \text{ V}$. The modulation index of the given $AM$ wave is .......