The need for modulation is

In an $AM$ wave,the carrier power is given by:

The amplitude of the upper and lower sidebands of an $A.M.$ wave,where a carrier signal with frequency $11.21 \, MHz$ and peak voltage $15 \, V$ is amplitude modulated by a $7.7 \, kHz$ sine wave of $5 \, V$ amplitude,are $\frac{a}{10} \, V$ and $\frac{b}{10} \, V$ respectively. Then the value of $\frac{a}{b}$ is $....$

Long range radio transmission is possible when the radio waves are reflected from the ionosphere. For this to happen,the frequency of the radio waves must be in the range:

$A$ message signal of $12 kHz$ and peak voltage $20 V$ is used to modulate a carrier wave of frequency $12 MHz$ and peak voltage $30 V$. Then,the modulation index is

$A$ radar has a power of $1 \ kW$ and is operating at a frequency of $10 \ GHz$. It is located on a mountain top of height $500 \ m$. The maximum distance up to which it can detect an object located on the surface of the earth (Radius of earth $= 6.4 \times 10^6 \ m$) is ....... $km$.