I got 95.67 percentile in Jee Mains 2019 and a rank of 48464 and I have got 96% in CBSE boards 2019.
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Hello kartikey, yes you can get some nit's and some iiit while you have scored good percentile in jee mains. You may get into nit Patna ,nit Jaipur.
Your percentile is good. And your rank is bit high.
As per the previous year cutoffs you have good chance of of getting admission to the medium ranked NITs such as NIT Nagpur, NIT Raipur, NIT Bhopal, NIT Rourkela,etc.
But you should not expect higher branches.
If you want higher branches then you can get lower ranked NITs such as NIT Patna, NIT Durgapur, NIT Uttarakhand, NIT Goa, NITs from North-east,etc
And some IIITs such as IIIT Jabalpur, IIIT Nagpur, IIIT kancheepuram, IIIT Pune,etc
All the best
You can also check for Colleges on the link below
https://engineering.careers360.com/jee-main-college-predictor
JEE Main 2025 College Predictor
Know your college admission chances in NITs, IIITs and CFTIs, many States/ Institutes based on your JEE Main result by using JEE Main 2025 College Predictor.