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is this correct?

Which are the different methods by which you can search...

or

What are the different methods by which you can search...

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They are both fully grammatical and idiomatic, with hardly any difference in meaning.

The slight difference is that "which" implies that the various different methods are already known, or have been described, and the recipient is being asked to select one or more of them. "What" implies that available methods have not already been mentioned, and is asking for new information.

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    You really shouldn't be answering such blatantly unresearched questions. And blatantly duplicate.
    – curiousdannii
    Commented Aug 15, 2016 at 21:57

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