If the amplitude of the modulated wave and the amplitude of the signal are equal, then the modulation index is .....$\%$

An amplitude modulated wave is represented by $10[1+0.6 \sin(40 \times 10^3 t)] \sin(4 \times 10^6 t)$ volt,where $t$ is in seconds. The ratio of the upper sideband frequency to the lower sideband frequency is:

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:

Range of frequencies allotted for commercial $FM$ radio broadcast is

$A$ message signal is super-imposed with a carrier signal. The resulting modulating signal $C_m(t)$ is given by $C_m(t)=A_1 \sin \left(\omega_1 t\right)+A_2 \sin \left(\omega_2 t\right)-A_2 \sin \left(\omega_3 t\right)$,where $\omega_2 < \omega_1 < \omega_3$. The modulation index and the angular frequency of the message signal respectively,are

For transmitting a signal of frequency $1 \text{ kHz}$,the wavelength of the wave should be: