In amplitude modulation,the amplitude of the carrier wave is $A_c$ and that of the modulating signal is $A_m$. In practice,the ratio of $A_m$ to $A_c$ is kept less than or equal to $1$ to avoid:

In an $AM$ wave,the carrier power is given by:

The mathematical form of an $AM$ wave is given by $e = 50 (1 + 0.5 \sin (2\pi \times 5 \times 10^{3}) t) \sin (31.4 \times 10^{6}) t \, V$. To generate this $AM$ wave,the amplitudes of the carrier wave and the modulating wave must be,respectively,....... and ....... .

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?

$List-I$	$List-II$
$A.$ Facsimile	$I.$ Static Document Image
$B.$ Guided media Channel	$II.$ Local Broadcast Radio
$C.$ Frequency Modulation	$III.$ Rectangular wave
$D.$ Digital Signal	$IV.$ Optical Fiber

Choose the correct answer from the following options:

If modulation index $\mu = \frac{1}{2}$ and $V_{m} = 2$,then $V_{c} = \, ?$