An optical fibre communication system works on a wavelength of $1.3 \mu m$. The number of subscribers it can feed if a channel requires $20 \ kHz$ is:

$A$ carrier wave is used to transmit a message signal. If the peak voltage of the modulating signal and the carrier signal are increased by $1 \%$ and $3 \%$ respectively,the modulation index is changed by (in $\%$)

The antenna current of an $AM$ transmitter is $8 \ A$ when only the carrier is sent,but it increases to $8.96 \ A$ when the carrier is modulated by a sine wave. The percentage of modulation is: (in $\%$)

The amplitude of the side bands of the modulated signal, if the carrier signal and message signal amplitudes are $25 \,V$ and $5 \,V$ respectively, is (in $\,V$)

$A$ message signal is used to modulate a carrier frequency. If the peak voltages of the message signal and carrier signal are increased by $0.1 \%$ and $0.3 \%$ respectively,then the percentage change in the modulation index is

In amplitude modulation,the message signal $V_{m}(t) = 10 \sin(2 \pi \times 10^{5} t) \text{ V}$ and the carrier signal $V_{c}(t) = 20 \sin(2 \pi \times 10^{7} t) \text{ V}$. The modulated signal contains the message signal with lower sideband and upper sideband frequencies. Therefore,the bandwidth of the modulated signal is $\alpha \text{ kHz}$. The value of $\alpha$ is: