Yes you can easily get admission in NIT Patna with this rank under home state quota. Though you might not get a CSE seat as the cutoff for cse in year 2017 was 7229 but you could easily get other core branches like mechanical, EE, ECE, Civil etc.
All the best.
Thank you.

Hello Aspirant ,

Talking about your rank you can definately opt for Nit patna as not only you will get benifit of your rank as well as state quota. You can even opt for better nits than that . Use the college predictor for better help for you . 

https://engineering.careers360.com/jee-main-college-predictor

Good luck.

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