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Hello Aspirant,
See the score i.e. 51 is nothing but your overall NTA score or percentile and it is the percentage of candidates scored less than or equal to you in your shift.
See it is quite difficult to tell you an exact figure of your rank because it keeps on changing every year depending upon various factors but yes we can help you with approximate figures on the basis of analysis of previous year's data.
So if we go through the analysis of marks Vs Percentile Vs rank for JEE-Main 2021 then according to the percentile mentioned by you in the question your rank is expected to be in the range of 501270 - 563500 .
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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 JEE-Main score or rank you can use JEE-Main College Predictor:-
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
Or
You can also check out our Engineering Counselling Subscription package in which you get B.Tech companion tool which will guide you in all your counselling and admission related issues and along with this you will be getting 3 one-to-one counselling sessions by our experts :-
https://www.careers360.com/campaign/Engineering-Counseling-Subscription
I hope this information helps you.
Good Luck!!
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