Hello,
Congratulations for your good will to reach upto 85 percentile.
But sorry sorry to say that since you are belongs to general category, you have very low chances to get into the NITs or GFTIs.
And yes you can get into the good private institutions on the basis of the jee mains exam.
Some of the good institutions are
GITAM UNIVERSITY
THAPAR UNIVERSITY
LOVELY PROFESSIONAL UNIVERSITY
Which are dome of the private institutions and you can also try in SASTRA UNIVERSITY  which I reccomend as one of the best engineering institution in india.

ALL THE BEST!!!
For any further queries let me know.

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