"He lives in a capital."
Translation:Він живе в столиці.
This is another sentence that has - to me - that ring of artificiality that defines it as one most likely composed by a foreigner. It's perfectly grammatical and correct but just unlikely as something that anyone would actually say. Much more likely "He lives in the capital" - because this means something quite specific and so is potentially a useful piece of information. This sentence means something different of course but the fact that someone lives in 'a capital', 'any capital', is just unlikely to be a useful or meaningful piece of information (although, yes, it conceivably could in certain very specific contexts).