If a signal of frequency $3 \ kHz$ is to be transmitted via amplitude modulation,which of the following should be chosen as the carrier wave frequency?

In a communication system operating at a wavelength of $800\,nm,$ only one percent of the source frequency is available as signal bandwidth. The number of channels accommodated for transmitting $TV$ signals of bandwidth $6\,MHz$ is (Take velocity of light $c = 3 \times 10^8\,m/s$)

The amplitude of $15 \sin (1000 \pi t)$ is modulated by $10 \sin (4 \pi t)$ signal. The amplitude modulated signal contains frequency(ies) of
$A) 500 \text{ Hz}$
$B) 2 \text{ Hz}$
$C) 250 \text{ Hz}$
$D) 498 \text{ Hz}$
$E) 502 \text{ Hz}$
Choose the correct answer from the options given below:

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. $AM$ Broadcast	$I$. $88-108\,MHz$
$B$. $FM$ Broadcast	$II$. $540-1600\,kHz$
$C$. Television	$III$. $3.7-4.2\,GHz$
$D$. Satellite Communication	$IV$. $54-890\,MHz$

Choose the correct answer from the options given below:

$A$ carrier is simultaneously modulated by two sine waves with modulation indices of $0.3$ and $0.4$; then the total modulation index is

$A$ $TV$ transmitting antenna is $98\,m$ high and the receiving antenna is at the ground level. If the radius of the earth is $6400\,km$,the surface area covered by the transmitting antenna is approximately $.........\,km^2$