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Most people use いろいろ質問する. But if I analyze it, いろいろ is な形容詞.

So I think it should be いろいろな質問する. What do you think?
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2015-05-31T11:16:54.983
24672
2015-05-31T12:10:00.793
9896
question
grammar
いろいろ質問する versus いろいろな質問する
* いろいろ can be used as a standalone adverb. (e.g. 色々話す, 色々ある, ...)
  * 質問する without を is a _verb_ , and it cannot be directly modified by the dictionary form of an adjective. (See [this similar question](https://japanese.stackexchange.com/a/4007/5010) on 勉強する/勉強をする)

Thus, these three phrases are all natural:

  * いろいろな質問をする
  * いろいろ質問をする
  * いろいろ質問する

But this phrase is non-standard:

  * いろいろな質問する
CC BY-SA 3.0
2015-05-31T11:57:15.843
24674
2015-05-31T12:10:00.793
2017-04-13T12:43:44.397
-1
5010
24672
answer
いろいろ can also be considered an adverb.

If you are describing the **types** of questions, いろいろな質問 would be correct.
But in the case of いろいろ質問する, you are talking about the **action** of asking
different things, and thus doesn't require な.
CC BY-SA 3.0
2015-05-31T12:04:37.650
24677
2015-05-31T12:04:37.650
10226
24672
answer