This grammar pattern is used to show that the speaker cannot decide to do something or be sure about something. It can be used with a past tense(‘-었을지/았을지/였을지 모르겠다’) and a noun(‘-일지 모르겠다’).
● 길이 막혀서 버스가 제시간에 도착할지 모르겠어요. (I’m not sure whether the bus can arrive on time because the traffic is heavy.)
● 아버지께서 식사를 하셨을지 모르겠군요. (I don’t know whether my father had a meal or not.)