~는지를 >> ~는지 + 를(object particle)
를 is used because ~는지 is an object of the verbs like 알다, 모르다, 말하다, 물어보다 ...
But, 를 is usually omitted for easy pronunciation. It is used when emphasizing ~는지.
문제가 있는지 물어보세요. Ask (them) whether there is a problem.
문제가 있는지를 물어보세요. Ask (them) WHETER there is a problem.
From
http://talktomeinkorean.com
Whether or not / -(으)ㄴ/는지
The verb ending -(으)ㄴ/는지 is basically used with verbs related to knowing, guessing, informing, thinking, etc, for expressing the meaning “whether or not”.
It can also be used with words such as 누구 (who), 어디 (where), 어떻게 (how), 왜 (why), 언제(where), 뭐 (what) and 얼마나 (how + adverb/adjective) to mark the end of a question inside a compound sentence.
Conjugation:
(1) Action verbs
- Verb stem + -는지
e.g.
먹다 → 먹는지
사다 → 사는지
(2) Descriptive verbs
- Verb stems ending with a vowel + -ㄴ지
(The verb 이다 (to be) is included in this category as well.)
e.g.
크다 → 큰지
예쁘다 → 예쁜지
- Verb stems ending with a consonant + -은지
e.g.
작다 → 작은지
좁다 → 좁은지
e.g.
뭐가 좋아요? (= What is good?) + 몰라요. (= I don’t know.)
→ I don’t know what is good. = 뭐가 좋은지 몰라요.
뭐가 좋다 → 뭐가 좋 + -은지 → 뭐가 좋은지→ 뭐가 좋은지 몰라요.
문제가 있다 (= There is a problem.) + 물어보세요. (= Ask.)
→ Ask (them) whether there is a problem. = 문제가 있는지 물어보세요.
문제가 있다 → 문제가 있 + -는지 → 문제가 있는지 → 문제가 있는지 물어보세요.
e.g.
내일 우리 만날 수 있는지(를) 알고 싶어요.
= I want to know whether we can meet tomorrow or not.
제가 왜 걱정하는지(를) 몰라요?
= Do you not know why I worry?