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Private engineering colleges in India conduct an entrance exam of their own for admissions. They don't have reservations for any category. 82 is a decent percentile but it is mandatory to write the entrance exams. A few reputed colleges are-
and many more. Kindly use the following link which will help you predict the colleges you can apply to using your JEE Mains percentile.
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
I hope this helps.
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