Step 1: Break down the phrase.
"Delusions of greatness" means false beliefs that one is extremely powerful, important, or great.
Step 2: Match the word.
"Megalomaniac" literally comes from "megalo" (great) and "mania" (obsession), meaning a person obsessed with, or deluded about, their own power, importance, or greatness. This is an exact match.
Step 3: Eliminate other options.
A "kleptomaniac" has an uncontrollable urge to steal, unrelated to delusions of greatness. A "romantic" is idealistic or affectionate in temperament. A "hypochondriac" is someone who is excessively anxious about having a serious illness, even without symptoms. An "ascetic" is a person who practices strict self-discipline and avoidance of worldly pleasures. None of these describe delusions of greatness.
Step 4: Confirm the answer.
The correct word is "megalomaniac", option (a).