From www.howtostudykorean.com
~ㄴ/은가(요) gets added to the stem of adjectives. Using this form makes a question a little bit softer than using the forms described previously. The exact difference cannot be translated perfectly, but sort of like how “would it be okay if I go into the park?” sounds slightly softer than “can I go into the park.”
You add ~ㄴ/은 to adjective stems just like you would when conjugating it to describe a noun:
예쁘다 + ㄴ/은 = 예쁜
작다 + ㄴ/은 = 작은
And then attach “가(요)” after that construction:
예쁜가(요)?
작은가(요)?
It is only conjugated into the present tense and therefore usually only used to ask about some sort of present situation. For example:
그 여자는 예쁜가? = Is that girl pretty?
이것은 너무 작은가요? = Is this too small?
그 학교가 좋은가? = Is that school good?
일이 너무 복잡한가요? = Is this work/task too complicated?
~ㄴ/은가(요) is commonly added to 이다 as well. For example:
그 사람이 선생님인가? = Is that person a teacher?
그 사람이 우리 엄마인가? = Is that person our mom? (Is that our mom?)
아닌가(요)? Is very commonly used at the end of a full sentence to say “no?” when you are asking yourself a question as if you are doubting yourself. For example:
그 여자는 한국에서 가장 예쁜 여자야. 아닌가? = That girl is the most beautiful girl in Korea… no?/isn’t she?
너무 복잡해! 아닌가? = This is too complicated. Isn’t it?
Using ~나(요) at the end of a sentence to ask a question has the same function of ~ㄴ/은가(요). That is, it can be used to make a question sound slightly softer than the other ways to ask a question. However, ~나(요) is more often used with verbs and with 있다 and 없다. For example:
Notice that the ㄹ irregular needs to be applied in appropriate situations again:
밥이 있나? = Is there rice?
사과도 여기서 파나요? = Do you sell apples here too?
소녀시대 콘서트를 여기서 하나요? = Is the Girl’s Generation concert here?
지하철을 타고 있나요? = Are you on (riding) the subway now?
This form can be used in the past tense as well. For example:
교통카드가 있었나요? = Did you have your bus (transportation) card?
그 소식을 들었나요? = Did you hear that/the news?