Yes, it would. It has to do with whether you negate the noun or the verb.
The question has no answer = Frågan har inget svar
The question does not have an answer = Frågan har inte svar
ingen/inget/inga are "no" before a noun or "none" on it's own. Ie "I have no friends" (jag har inga vänner) or "Do you have any friends? I have none." (har du några vänner? Jag har inga). It's a lot like how in English we say both my and mine, but in Swedish the just say min/mitt/mina depending on the grammar of the object.
As standalone words, ingen call also mean "nobody" and "inget" can mean "nothing"
(Someone feel free to correct me if I am wrong or unclear)
although they can both be used interchangably, right? (not for purposes of this exercise, but in real life?)