Each scheme is matched to the single respect in which it is best: a-iii, b-i, c-iv, d-ii — option 2.

a — FM's power efficiency. Its envelope is constant, so the transmitter's output stage can be run in class C or saturated switching — 70 % efficient or better — whereas a linear AM stage must stay linear and wastes power doing so. FM also converts extra bandwidth into signal-to-noise improvement, so a given quality is achieved with less transmitted power.

b — SSB for voice. The two sidebands of an AM signal carry identical information, so one is pure redundancy. Removing it halves the occupied bandwidth to \(f_{m}\) and removing the carrier saves the two-thirds of power AM spends on it. Speech tolerates this well because it has no significant energy near DC — the audio band starts around 300 Hz — leaving room for the filter to cut cleanly between the sidebands. This is why long-distance HF voice communication is almost entirely SSB.

d — why VSB exists, and why it is not simply SSB. This is the pairing that explains the whole question. When a signal does have energy down to DC — television video is the standard case — SSB becomes impossible: the two sidebands meet at the carrier with no gap, and no filter can separate them without destroying the low-frequency content that carries the picture's average brightness. VSB is the compromise: transmit one sideband fully, plus a small vestige of the other, so the filter's gradual roll-off is symmetrical about the carrier and the low frequencies are recovered correctly. It costs a little more bandwidth than SSB but far less than DSB.

c — AM's one advantage. A diode, a capacitor and a resistor recover the envelope. That receiver simplicity is the entire justification for transmitting a carrier that carries no information, and it is why AM broadcasting outlived its inefficiency: transmitter power is spent once, while receivers are bought by millions.

Hence, the correct code is a-iii, b-i, c-iv, d-ii.