The electron density of $E, F_1, F_2$ layers of the ionosphere is $2 \times 10^{11} \, m^{-3}$,$5 \times 10^{11} \, m^{-3}$,and $8 \times 10^{11} \, m^{-3}$ respectively. What is the ratio of critical frequencies for the reflection of radio waves?

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

Given below are two statements:
Statement-$I$: $A$ speech signal of $2 \, kHz$ is used to modulate a carrier signal of $1 \, MHz$. The bandwidth requirement for the signal is $4 \, kHz$.
Statement-$II$: The sideband frequencies are $1002 \, kHz$ and $998 \, kHz$.
In the light of the above statements,choose the correct answer from the options given below:

The size of the antenna required for a carrier wave of frequency $3 \text{ MHz}$ is: (in $\text{ m}$)

The $TV$ transmission tower at a particular station has a height of $125\, m$. For doubling the coverage range,the height of the tower should be increased by .............$m$.

The figure shows the waveform of an amplitude modulated wave. Its modulation factor is