If you subtract from the carrier frequency the frequency of the tone that modulates it, then filter out the carrier frequency, then you have a lower sideband frequency. If you add to the carrier frequency, filter out the carrier, then you have an upper sideband frequency.

in frequency modulation, frequency of carrier signal changes. so frequency variations of carrier convey all the information in frequency modulation.

Explain the need for carrier frequency stability in radio transmitters?

probably

(the carrier frequency +- the maximum frequency of the pulse train)/(the carrier frequency)

but pulses have a lot of harmonics