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Hello Dear,
As the percentile mentioned by you is not enough for you to fetch you any college on this percentile but you will definitely get private college the cut off depends upon the number of seats available, the difficulty level of paper and number of candidates writing the examination. And, hence varies every year depending on these factors.
You can check our predictors link to know more about the college which you can get
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
Good Luck
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