The height of a $TV$ transmitter antenna is $100 \ m$. What is the area covered by the transmitter for broadcasting? $(R = 6.4 \times 10^{6} \ m)$

The circuit used to separate information signals from the carrier wave is called a .......

Statement-$1$: Sky wave signals are used for long-distance radio communication.
Statement-$2$: These signals are generally less stable than ground wave signals.

$A$ carrier signal of frequency $v_1$ and peak voltage of $V_1$ is modulated by a message signal of frequency $v_2$ and peak voltage of $V_2$. Let $m$ be the modulation index and $v_{+}, v_{-}$ be side bands produced. The correct statement is

$A$ bandwidth of $6 \, \text{MHz}$ is available for $A.M.$ transmission. If the maximum audio signal frequency used for modulating the carrier wave is not to exceed $6 \, \text{kHz}$,the number of stations that can be broadcasted within this band simultaneously without interfering with each other will be ..... .

The maximum amplitude of an $AM$ wave is $90 \ V$ and the minimum amplitude is $10 \ V$. What is the modulation index of the $AM$ wave in percentage?