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Hello Aspirant,
Actually the NTA score is nothing but your percentile because NTA score is called as percentile or raw score so based on that percentile we can help you with you expected rank range.
So If we go through the analysis of marks Vs Percentile Vs rank for JEE-Main 2020 then according to the percentile mentioned by you in the question your rank is expected to be in the range of 259093 - 291258 .
You can check out marks Vs ranks Vs Percentile from the link given below :-
https://engineering.careers360.com/articles/jee-main-marks-vs-percentile
Or
You can also use JEE-Main Rank Predictor to predict your rank and percentile :-
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JEE Main Rank Predictor - Know your expected IIT JEE Main 2021 Rank by ...
Note that the rank which is predicted is only the expected rank on the basis of previous year's data so your actual rank might vary depending upon current factors.
To have a list of all those colleges which you can get based upon your marks, category, and state you can use JEE-Main College Predictor:-
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
If you are preparing for JEE-Main 2021 (remaining attempt) or 2022 then I would recommend you to check the resources made by our experts to help aspirants like you in the best and smart preparation of JEE-Main 2021 or 2022 :-
https://learn.careers360.com/jee-main-coaching/?utm_source=%20QnA
I hope this information helps you.
Good Luck!!
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