I sense that using "なん" in questions probably makes the question sound more formal:
"どこなんですか?" // maybe more formal?
"いつなんですか?" // maybe more formal?
"だれなんですか?" // maybe more formal?

Am I right about this? Maybe this is very similar to the function of [美化語]{びかご}?

But, I don't remember ever seeing this in written Japanese. I suspect that this is just because using fewer characters trumps whatever formality "なん" may, or may not, inject into questions?

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    なんなんですか? (filler) – istrasci Nov 21 '13 at 18:33
  • No, you can add なん to the question なんですか as you did with the other question words. 何なんですか = 何なのですか. – istrasci Nov 21 '13 at 22:08
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    It is quite the opposite of what you appear to be thinking. なん is very informal. When you start hearing lots of ん's and small っ's, that is a good sign of when we have gone informal. – l'électeur Nov 22 '13 at 3:54

I don't think なん is particularly formal. It's short for なの. If I understand the traditional grammar right, な here is analyzed as 断定の助動詞「だ」の連体形「な」, a form which appears chiefly before the 形式名詞「の」 in constructions such as 「〜なのだ」「〜なので」「〜なのに」「〜なのか」 and so on.

I think it's like this:

 どこ + のだ = どこのだ

So the difference in meaning is the same you get from adding 〜のだ to a sentence.

If you take the above and change だ to です and add か, then you've almost got your original example. You just need to change の to ん:

 どこなですか → どこなですか

I think that this の can change to ん before forms of the copula and before the question particle か, but like most reduced forms it's less formal than the full version. It can even be reduced to ん at the end of a sentence in certain dialects, but you should be aware that this is not considered standard Japanese.

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