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It is still not clear to me what is the difference between ~じゃないか and ~じゃないのか. The answer to this old question of mine mentions that they are pretty much interchangeable and I wish to learn more details. What are the different meanings of ~じゃないのか gives?

Compared to ~じゃないか, I have an impression that the ~じゃないのか indicates that the speaker assumes that the preceding clause is not true. Is it true in general?

For example, 中村さんは童貞じゃないか means "Nakamura-san is a virgin!" while 中村さんは童貞じゃないのか means something like "Nakamura-san is not a virgin?!?" and the speaker assumes that Nakamura-san is a virgin.

Here is another example for this sense of じゃないのか:

お前もこの映画がヒットした方が何かと都合が良いんだろ?だから頼んでもないのにわざわざ関与してくるんじゃないのか?(Oshi no ko ch. 127 pg. 14)

It will be convenient for you when this movie gets popular, right? So, you get involved with me even though I didn't ask for it, no?

I hope my translation is correct here. Also, I believe that じゃないのか here can be substituted with じゃないか with no change in meaning (?).

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  • The answer to this old question of mine mentions that they are pretty much interchangeable: No, what @naruto said is that they "are sometimes interchangeable" (sic.); to be clearer, your translations might be correct but your example 中村さんは童貞じゃない + /のか could be correctly translated as "I didn't know Mr. Nakamura wasn't virgin" in both cases, depending on the intonation. Commented May 8 at 21:48

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Compared to ~じゃないか, I have an impression that the ~じゃないのか indicates that the speaker assumes that the preceding clause is not true. Is it true in general?

The difference between V-か and V-のか in a yes-no question is, generally speaking, the former is a "fresh" question, that is neutral on truthiness of V, while the latter presents V as an "unexpected" fact (to the speaker) and request confirmation by hearer, thus used when the speaker already has some bias, which is negative of V.

Then as you may suspect, the negative form of V-か (V-ないか) would be logically redundant, so this form is instead usually employed for lower-probability variant of positive V-か. With the above, ~じゃないか? means "is ... perhaps —?" and ~じゃないのか? means "(I thought) ... is —, but isn't it true?". In some situations you can use them interchangeably, but of course other times not.

だからわざわざ関与してくるんじゃないのか? That's why (you) intentionally get involved with me, isn't it?
だからわざわざ関与してくるんじゃないか? Is it perhaps why (you) intentionally get involved with me?

By the way,

For example, 中村さんは童貞じゃないか means "Nakamura-san is a virgin!" while 中村さんは童貞じゃないのか means something like "Nakamura-san is not a virgin?!?" and the speaker assumes that Nakamura-san is a virgin.

This example is ill-formed because you seem comparing a non-question and a question. As the previous answer shows, they both have question and exclamatory (via rhetorical question) usages, but it complicates matter a lot with idiomatic senses, so you might open a new question if you want to delve into it. The accurate comparison would be:

中村さんは童貞じゃないか? Is Nakamura-san perhaps a virgin?
中村さんは童貞じゃないのか? Is Nakamura-san really not a virgin?

中村さんは童貞じゃないか! So Nakamura-san is a virgin!
中村さんは童貞じゃないのか! What? Nakamura-san is (in fact) not a virgin!

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