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I would like to know is there any way to search for protected questions like duplicate etc.

From advanced search:

status  closed:yes
        duplicate:no
        migrated:no
        wiki:no

I have tried: protected:yes

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Short answer: you can't; such operator is not mentioned anywhere in How do I search? and there's a pending feature-request for that on Meta.SE since 2010.

However this SEDE query seems to be working (topn = number of questions to be shown in the results).

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