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Hello!!!
As per your rank and percentile, college and branch available for you is only Mathematics in nit patna as the your rank is quite high due to which it's difficult to get a college and branch of your choice.
You may check this link for more information regarding nit patna.
https://www.google.com/amp/s/engineering.careers360.com/articles/jee-main-cutoff-for-nit-patna/amp
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