A message signal of frequency 20 kHz and peak voltage of 20 volt is used to modulate a carrier wave of frequency 1 MHz and peak voltage of 20 volt. The modulation index will be :

A carrier wave V_c(t) = 160 sin(2$$\pi$$ $$\times$$ 10⁶t) volts is made to vary between V_max = 200 V and V_min = 120 V by a message
signal V_m(t) = A_m sin(2$$\pi$$ $$\times$$ 10³t) volts. The peak voltage A_m of the modulating signal is ___________.

A TV transmission tower antenna is at a height of 20 m. Suppose that the receiving antenna is at.

(i) ground level

(ii) a height of 5 m.

The increase in antenna range in case (ii) relative to case (i) is n%.

The value of n, to the nearest integer, is ___________.

For VHF signal broadcasting, ___________ km² of maximum service area will be covered by an antenna tower of height 30 m, if the receiving antenna is placed at ground. Let radius of the earth be 6400 km. (Round off to the Nearest Integer) (Take $$\pi$$ as 3.14)