hi,

see cutoff score changes every year and it depends on certain factors like number of applicants, questions difficulty level, seat matrix, students category. however there is separate cutoff available as per home state quota and all india quota.

last years home state quota opening and closing rank for nit patna

OBC-NCL  3232 - 3900

All india quota opening and closing rank

obc ncl 3051- 3828

however to get the complete list of college name based on your category and score please enroll for careers360 jee main paper 2 college predictor tool,

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