For transmitting a signal of frequency $1000 \text{ kHz}$, the minimum length of the antenna is (in $\text{ m}$)

$A$ message signal of peak voltage $12 \ V$ is used to amplitude modulate a carrier signal of frequency $1.2 \ MHz$. The amplitude of the side bands is (in $V$)

An audio signal $v_{m} = 20 \sin(2 \pi \times 1500 t)$ amplitude modulates a carrier $v_{c} = 80 \sin(2 \pi \times 100,000 t)$. The value of percent modulation is..........

For sky wave propagation,the radio waves must have a frequency range in between

Which frequency range is suitable for sky wave propagation?

Which of the following is $NOT$ a reason for why we need modulation in communication systems?