$A$ message signal of peak voltage $12 \ V$ is used to amplitude modulate a carrier signal of frequency $1.2 \ MHz$. The amplitude of the side bands is (in $V$)

To radiate a wave of frequency $1 \text{ kHz}$ efficiently,what should be the minimum length of the antenna in $km$?

We do not transmit low frequency signals to long distances because:
$(a)$ The size of the antenna should be comparable to signal wavelength,which is impractical for a signal of longer wavelength.
$(b)$ Effective power radiated by a long wavelength baseband signal would be high.
$(c)$ We want to avoid mixing up signals transmitted by different transmitters simultaneously.
$(d)$ Low frequency signals can be sent to long distances by superimposing them with a high frequency wave.
Therefore,the most suitable options are:

In amplitude modulation,the modulation index $m$ is kept less than or equal to $1$ because

The height of a $TV$ tower is $150 \ m$. If the population density in the area covered by the $TV$ tower is $50 \ \text{lakhs}$, then the population density around the $TV$ tower is ....... $km^{-2}$. (Radius of the Earth is $6.4 \times 10^{6} \ m$)

For amplitude modulated wave broadcast, which of the following conditions is suitable?