In a communication system,noise is most likely to affect the signal:

Given below are two statements
Statement $I:$ For transmitting a signal,the size of the antenna $(l)$ should be comparable to the wavelength of the signal (at least $l = \frac{\lambda}{4}$ in dimension).
Statement $II:$ In amplitude modulation,the amplitude of the carrier wave remains constant (unchanged).
In the light of the above statements,choose the most appropriate answer from the options given below.

$A$ message signal of frequency $15 kHz$ is used to modulate a carrier of frequency $v_c$. If the side bands produced are $1515 kHz$ and $1485 kHz$,then $v_c$ is (in $MHz$)

$A$ speech signal of $3 kHz$ is used to modulate a carrier signal of frequency $1 MHz$,using amplitude modulation. The frequencies of the side bands will be

$A$ signal is to be transmitted through a wave of wavelength $\lambda$,using a linear antenna. The length $l$ of the antenna and effective power radiated $P_{eff}$ will be given respectively as: ($K$ is a constant of proportionality)

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