Hi Ujwal 

Since my Hometown is Darbhanga.So i know Darbhanga pretty well.

I am giving you all the government college in Darbhanga,Bihar.

1) Darbhanga College of Engineering (for      Engineering)

2) Darbhanga Medical college (For medical)

3) Kameshwar Singh Darbhanga Sanskrit University

4) Lalit Narayan Mithila University

5) Women's Institute of Technology (Affiliated from LNMU Darbhanga)

All the best

Hope it Helps