Hello Dear,

As per the marks mentioned by you your Percentile is between 82.01-86.90 and rank between 165679 - 120612.  Yes you are qualified in mans for private colleges and your rank is not good enough to give you any NIT/Government college. You can check the rank vs percentile vs marks below:

https://engineering.careers360.com/articles/jee-main-marks-vs-percentile

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