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Hello,
For sure you can give the jee mains exam. For your all kind of doubts you can follow the articl here:-
https://engineering.careers360.com/articles/how-to-fill-jee-main-application-form
For your question you have the section where it will be written like:- "Appeared or appearing for improvement of 12th exam" you have to write yes there.
Fill up the form as per the guide.
Hope it helps!
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