An audio signal of 15kHz frequency cannot be transmitted over long distances without modulation because

It is given that the frequency of the signal is .

Now, the wavelength is given by:

Now, the antenna has to be at least λ/4 i.e. 5 km.

It is not convenient to have such a huge antenna !

Hence, option (a) is correct and option (c) is incorrect.

The power radiated by the transmitter is proportional to

where l is the length of the antenna. The power radiated decreases with increasing wavelength and increasing length. If the antenna is less than 5km, then the power radiated will be less causing a weak and highly attenuated signal to reach at the receiver. Hence, option (d) is correct.

Sky waves are mode of transmission for signal with frequencies from a few MHz to 30-40 MHz. Now, the given signal is 15KHz or 0.015MHz. Thus, transmission via sky waves is not possible. Thus, option (b) is correct.