Hello aspirant!  Let me to inform you that there are various colleges in bihar that you can get through the bcece counseling process. So based on your rank you can get private colleges as well as government college. So if you want top government colleges like bhagalpur and muzaffarpur it has different cut off for different branches. You can check the here :

https://www.careers360.com/colleges/bhagalpur-college-of-engineering-bhagalpur/cut-off

https://www.careers360.com/colleges/muzaffarpur-institute-of-technology-muzaffarpur/cut-off