Hello dear

With this common Rank ; there may be chances to get seat in nit patna with home state quota.

And from your ews category rank; you have a fair chance to get seat in nit patna ; but don't depend only on this because it will depend upon other students choices and preferences because this category is introduced first time .

So take another option along with this and be safe .

You can see last year scut offs and have thought about it .:

https://engineering.careers360.com/articles/jee-main-cutoff-for-nit-patna/amp

Good luck