합니까? and 하십니까? are both correct. 합니까? is the question form of 합니다, which is a formal and polite ending form of the verb 하다(do). 하십니까? and its declarative form 하십니다 are similar, but they are based on 하시다 instead of 하다. 하시다 is what's called an "honorific" verb. It conveys a sense of respect for the subject of the verb. Honorific forms are typically created by adding 시 to the verb stem (가다->가시다, 타다->타시다, 읽다->읽으시다). Examples: 1. 동생이 운동을 합니다 / 동생이 운동을 합니까? (Is your little brother exercising?) 2. 아버지가 운동을 하십니다 / 아버지가 운동을 하십니까? (Is your father exercising?) 3. 친구가 찾아왔습니다. (찾아오다 -> 찾아왔습니다) 4. 어머니 친구가 찾아오셨습니다. (찾아오시다 -> 찾아오셨습니다) In #2 and #4, we use the honorific versions because the subject is one's father or a friend of one's mother.