The height of a $TV$ transmission tower is $240 \ m$. Up to what distance can the transmission be received (in $km$)? (Radius of the Earth $R = 6.4 \times 10^6 \ m$)

$A$ carrier wave of peak voltage $15 V$ is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of $80\%$ (in $V$)?

$A$ modulated signal $C_m(t)$ has the form $C_m(t) = 30 \sin(300\pi t) + 10 \cos(200\pi t) - 10 \cos(400\pi t)$. The carrier frequency $f_c$,the modulating frequency $f_m$,and the modulation index $\mu$ are respectively given by:

The refractive index of the ionosphere:

$A$ radio can tune to any station in the $6\,MHz$ to $10\,MHz$ band. The value of the corresponding wavelength bandwidth will be $....\,m$.

The height of a transmitting antenna at the top of a tower is $25 \; m$ and that of the receiving antenna is $49 \; m$. The maximum distance between them for satisfactory communication in $LOS$ (Line of Sight) is $K \sqrt{5} \times 10^{2} \; m$. The value of $K$ is $\dots$ [Assume radius of Earth is $64 \times 10^{5} \; m$] (Calculate up to the nearest integer value).