The function of a detector is to demodulate the modulated carrier wave and the steps for this process are

$A$ sinusoidal carrier voltage of frequency $1.5 \, MHz$ and amplitude $50 \, V$ is amplitude modulated by a sinusoidal voltage of frequency $10 \, kHz$ producing $50 \%$ modulation. The lower and upper side-band frequencies in $kHz$ are:

Match List $I$ with List $II$ :

List $I$	List $II$
$A$. Attenuation	$I$. Combination of a receiver and transmitter.
$B$. Transducer	$II$. Process of retrieval of information from the carrier wave at receiver.
$C$. Demodulation	$III$. Converts one form of energy into another.
$D$. Repeater	$IV$. Loss of strength of a signal while propagating through a medium.

Choose the correct answer from the options given below:

$A$ 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

While tuning in a certain broadcast station with a receiver,we are actually

The minimum size of an antenna for transmitting electromagnetic waves at $1500 \text{ MHz}$ is