ᄂ 적이 있다 vs 본 적이 있다 - n jeog-i issda vs bon jeog-i issda

In the second sentence, you’ve added 아/어 보다 grammar, which means “trying”!

So there’s not much difference between the two sentences.

And the 을까요 is used to get the opinion of someone!

A better sentence is 시험을 쓰지 않을까? (But they mean the same)..

It’s okay to use this grammar in -ve format

L1.42 V-(으)ㄴ 적이 있다, V-아/어 본 적이 있다 grammar = have done, have tried ~express the experience of having done or tried something

Usage:
- V-(으)ㄴ 적이 있다 = having a certain experience in the past = have done
- V-(으)ㄴ 적이 있다/없다 = not having a certain experience in the past = haven't done

- V-(으)ㄴ 일이 있다/없다 expresses the same meaning as V-(으)ㄴ 적이 있다/없다, but V-(으)ㄴ 적이 있다/없다 is used more often.

- V-아/어 본 적이 있다 = express the past experience of having tried something = have tried
- V-아/어 본 적이 있다/없다 = express the experience of not having tried something = haven't tried

- These grammars are not used for describing things that are often repeated or are everyday occurrences.

Tense:
Verb + -(으)ㄴ 적이 있다/없다:
Verb ending in vowel + -ㄴ 적이 있다/없다
보다 -- 본 적이 있다/없다 (have seen)
타다 -- 탄 적이 있다/없다 (have ridden)
여행하다 -- 여행한 적이 있다/없다 (have traveled)
*만들다 -- 만든 적이 있다/없다 (have made)

Verb ending in consonant + 은 적이 있다/없다
읽다 -- 읽은 적이 있다/없다 (have read)
받다 -- 받은 적이 있다/없다 (have received)
먹다 -- 먹은 적이 있다/없다 (have eaten)
*듣다 -- 들은 적이 있다/없다 (have heard)

Verb + 아/어 본 적이 있다:
사다 -- 사 본 적이 있다 (have tried to buy)
먹다 -- 먹어 본 적이 있다 (have tried to eat)
공부하다 -- 공부해 본 적이 있다 (have tried to study)
여행하다 -- 여행해 본 적이 있다 (have tried to travel)
만들다 -- 만들어 본 적이 있다 (have tried to make)
*듣다 -- 들어 본 적이 있다 (have tried to listen)

Examples

1. 한국 드라마를 본 적이 있어요?
Have you seen Korean drama?

2. 회사에 지각한 적이 없어요.
I have never been late to work

3. 유럽에 가 본 적이 있어요?
- 네, 한번 가 본 적이 있어요.
Have you ever been to Europe?
- Yes, I have traveled there once.

4. 한국 음식을 먹어 본 적이 없어요.
I have never tried Korean food.

5. 시장에서 물건값을 잘 깎아요?
- 아니요. 깎아 본 적이 없어요.
Can you bargain well at the market?
- No, I have never been able to bargain.

6. 한국에 와서 병원에 간 적이 있어요?
- 네, 병원에 가 본 적이 있어요.
Have you gone to hospital in Korea?
- Yes, I have gone to hospital.

7. 여권을 잃어버린 적이 있어요?
- 아니요. 여권을 잃어버린 적이 없어요. 그렇지만 우산은 잃어버린 적이 있어요.
Have you lost your passport?
- No, I haven’t . But I have lost my umbrella.

8. 어릴때 병원에 입원한 적이 있어요.
I was hospitalized when I was a child.

9. 한국말을 몰라서 실수한 적이 있어요.
I've made a mistake because of my poor Korean.

I think the answer by Super Cool Handsome Gel Boy makes sense, so let me supplement it. In my opinion, 아/어 보다 could be translated as 'try ~ing' rather than 'try to'. But I am not so confident in my English, so I need English speakers' help.

According to my understanding, 'try ~ing' is used when you are doing something already or try to do something expecting some future influence. For instance,

I am trying going vegetarian. (I have already stopped eating meat for a while.)
Try being quiet. (Be quiet and keep quiet.)

If this understanding is correct, I can give an explanation. Two expressions would be translated as

ㄴ적이 있다: there was an event that ~ (better translated as 'have ever ~')
아/어 보다: try ~ing

If you are using the second expression in the past tense, you are saying that the action was already taken. So two sentences are basically the same in this case and can be used interchangeably. Of course you can combine two expressions.

아/어 본 적이 있다 (have ever tried ~ing).

I think the third expression is most common in Korea because it sounds somewhat polite. The following might be an answer to Rathony.

서울에 가려고 했는데 못 갔다. (correct)
I tried to go to Seoul but couldn't.
서울에 가 봤는데 못 갔다. (very weird and not recommended, could possibly be used by some comedians because 가다 could be interpreted as either 'go' or 'reach')
I tried going to Seoul but couldn't.
서울 방향으로 가 봤는데, 다리가 끊어져서 도착하지 못했다. (fixed)
I tried going toward Seoul, but couldn't reach it because the bridge was broken.

What’s this symbol?

The Language Level symbol shows a user's proficiency in the languages they're interested in. Setting your Language Level helps other users provide you with answers that aren't too complex or too simple.