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Hello aspirant,
Sorry to say but for the rank you got it is very difficult to get any branch in any Nit and IIIT's even with your category taken into consideration. However you can try for your State College Nit and can even try for some private institutions which offer admissions through jee main score.
You can check your chances for colleges in the following link,
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
Hope this helps
Good luck
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