Dear Aspirant 

Yes definitely you can work in Bihar as an engineer as you can do job as an engineer in the good companies whose branches are there in patna. You can also be posted as senior engineer in Indian Railway in Bihar, so there are lots of job opportunities available for engineers in bihar. So you don't have to worry about these things and just need to concentrate on your engineering.

Good luck for your future :) 

Feel free to ask if you have any further queries.