This is the 4178th most frequent Korean word.
주무
The Korean word "주무" is not complete on its own. It could be part of "주무시다," which is a honorific verb meaning "to sleep."
In this sentence, '주무시고' is the honorific form of '자다' (to sleep) used to show respect towards the grandfather.
할아버지께서 방에서 주무시고 계세요.
Grandfather is sleeping in the room.
Here, '주무시는' again serves as the honorific form of 'sleeping', modifying the action.
주무시는 동안 방에 들어가지 마세요.
Do not enter the room while (someone) is sleeping.
In this question, '주무셨나요' reflects the respectful inquiry about the sleeping experience.