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
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).