Yes you have a chance to grab govt engineering colleges in bihar,as per closing ranks of previous year you can get colleges like

•Bhagalpur college of engineering

•Mit muzaffarpur

And other colleges too.I cannot say that 100% but you have a chance to grab a college and also i can't say which branch,if you're not branch specific then no problem you will get a college.

All the best for future and hope this helps you.cheers.