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Yes, you can go some of the private colleges according to your rank, As it depends on your category your position decides.
To help you further,
Minimum percentile in jee main 2021 to qualify it to be eligible for jee advanced 2021 is given below :-
general :-87.8992241 percentile
EWS:- 66.2214845 percentile
OBC-NCL :- 68.0234447 percentile
SC :- 46.8825338 percentile
ST:- 34.6728999 percentile
PH :- 0.0096375 percentile
To know about the colleges tap the below link :
https://engineering.careers360.com/jee-main-college-predictor?utm_source=qna&utm_medium=jee_cp
It depends on your category.If u r general category then u will get middle or last clgs.If u belongs to reserved category u will definitely gets a top nit clgs
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