뭔가 = 무엇인가 = 무엇이다 (is something) + -ㄴ가 (phrase and sentence ending raising a question/doubt). -ㄴ가 can create a formal question that is vague and not specifically directed, primarily in writing. - 삶이란 무엇인가? = What is life? / What is this thing called life? - 우리가 가는 곳은 어디인가? = Where is the place we're going? It is also used at the end of a questioning or indefinite reference word (what, when, where, etc) to add the sense of doubt in a soft, self-directed tone. - 뭔가 (무엇인가) 잘못괸 게 트림없어 = It must be that something went wrong. - 친구는 어딘가 (어디인가) 슬퍼 보였다 = My friend had a sad look about him (somewhere I can't pinpoint). - 언젠가 (언제인가) 본 듯한 얼굴 = a face I might have seen before. (sometime I can't remember when) - 왠지(왜인지)/어쩐지 (어째서인지) 마음이 불안하다 = I feel insecure for some reason. The last one is using a variation -ㄴ지 which has a similar function. Both -ㄴ가 and -ㄴ지 can create the questioning phrase for different grammatical functions (뭔가 = subject (since 'what' is like a pronoun), 어딘가, 언젠가, 왠지, 어쩐지 = adverb, 뭔가를 = object (because the object marker 를 is added)).

‘뭔’가 is short form of ‘무엇’이(가) and means ‘something’ ‘ 뭔가 = 제가 모르는 일’이 있었어요? Is there something (happened) which I don’t know? and ‘가’ is subject case marker here. Unfortunatly it is so complicated to explain ‘why’. It is just the way Koreans speak. :D