The -지 in the construction 'verb stem + modifier 지 모르다' and the -지 in 'verb stem + 지 않다/못하다/말다' are not the same '지'. They just sound the same. For 'verb stem + 지 않다/못하다', the '-지' doesn't have any particular meaning on it's own. It's use is purely grammatical in certain negative structures. Note that the '-지' does nominalize what comes before so it's actually possible to add particles like -이/가, -은/는, -을/를, 도 to the '-지'. For example, "가지도 못했어요" would mean "I couldn't even go" or "별로 좋지가 않아요" would mean "It's not particularly good." This will no doubt be a bit of an oversimplification but the -지 in the construction 'verb stem + modifier 지 모르다' indicates possibility or knowledge. Note that you need a tense modifier before the '-지'. Whether you use -은/는 or -을/ㄹ affects the meaning and usage. With -은/는/ㄴ, the '-지' refers to the knowledge of what comes before. Some examples: 어디에 갔는지 모랄요 -> I don't know where it went 뭘 먹었는지 몰라요 -> I don't know what he ate 얼마나 비싼지 몰라요 -> I don't know how expensive it is 몇 시에 갔는지 몰라요 -> I don't know what time he left/went 잘하는지 몰라요 -> I don't know whether he does it well. With -을/ㄹ, it has a greater sense of possibility or uncertainty about something. You can add '도' on the end to emphasize that you think what precedes probably is/was/will be the case. Some examples: 갈지 몰라요 -> I may go (lit, I don't know whether I will go) 갈지도 몰라요 -> I may go (indicates greater likeliness that I will go) 갈지 안 갈지 몰라요 -> I'm not sure whether I'll go or not 밥을 이미 먹었을지도 몰라요 -> He may have already eaten 얼마나 비쌀지 몰라요 -> I don't know expensive it might be 비쌀지도 몰라요 -> It may be expensive (there is an implication here that the speaker suspects it is expensive). Please don't confuse the above with the 'verb stem + ㄴ/은 -지' construction indicating 'time since...' 고향에 간 지 오래 됐어요 -> It's been a long time since I went to my hometown. 밥을 먹은 지 2 시간 됐어요 -> It's been two hours since I last ate. Note that English has started to influence this expression so, sticking with the above examples, one could also say 고향에 안 간 지 오래 됐어요 -> I haven't gone to my hometown in a long time. 밥을 안 먹은 지 2 시간 됐어요 -> I haven't eaten in two hours. The intended meaning is really the same though some would consider the latter two examples not to be proper Korean.

Normaly if you put ~지 after Verb or adjective, this Verb+지 is changed to a Noun clause.. ~모르다.(Don't know) you need Object(Noun or Noun clouse) for this verb... 아는지(know +지) 모르다, 좋은지(good +지) 모르다. 바쁜지(busy + 지) 모르다. etc good luck!

Thank you :)

궁금해거든요 -> 궁금하거든요. '-거든' attaches directly to the verb stem so you don't need the '-어/아' in the middle.