Discussion
Which scheme offers no figure-of-merit improvement over the channel ratio?
Answer: C
SSB achieves unity, neither better nor worse than the channel, and DSB-SC matches it. Both angle schemes exceed unity substantially at large index, which is their whole point. And the last option is self-contradictory, since an index of five is wideband rather than narrowband. Recognising that the amplitude family's best case is merely to break even is the clearest way to see why angle modulation displaced it wherever bandwidth allowed. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.
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