Bihar

Bihar is one of the developing states in India and many colleges have started to establish this branch in their college for a better education. Recently Amity University established it.
But here is the list of best government college in Bihar which is quite better than private college
1. Bhagalpur College of Engineering, Bhagalpur
State Ranking:- 1 Established:-1960 Fee Rs. 50000 Per Year Strength:-5000 Total Faculty:-129 Highest package:- Rs 9 Lakh Per annum Total company visited in 2015:- 48 Company and 159+ placement
http://bcebhagalpur.ac.in/index-mobile.html
2.Darbhanga College of Engineering, Darbhanga
It is affiliated with the Aryabhata Knowledge University, Patna Est. in 2008 and approved by AICTE.
State Rank 2
Total Faculty:- 110
Intake Exams:- BCECE
http://www.dcedbg.org/
3. Indian Institute of Technology, Patna
The Indian Institute of Technology Patna is an autonomous institute of education and research in science, engineering and technology located in Patna, India Est. in 2008
https://www.iitp.ac.in/
Intake Exams: JEE Advanced, GATE
4. Darbhanga College of Engineering, Darbhanga
It is affiliated with the Aryabhata Knowledge University, Patna and approved by AICTE established in 2008.
http://www.dcedbg.org/
Intake Exams: BCECE
5. Dr Rajendra Prasad Central Agricultural University, Samastipur
This is one of 65 agriculture universities in India established in 1905. It is near Pusa Bazaar, in Samastipur District, Bihar.
http://www.pusavarsity.org.in/
Intake Exam:- BCECE

I am providing a list here. This list is not based on rankings, so research a bit before enrolling anywhere.
Consider the following factors:
Teaching methodology of the faculty members.
Infrastructure of the coaching centre.
Study materials for preparation.
Performances for the previous years.
Annual results.
Package of the coaching or fees.
So, here is the list:
http://entranceexaminfo.com/best-coaching-institute-for-bcece-2017-preparation/
Brilliant Tutorials
FIITJEE
Narayana Institute
Resonance
Aakash Institute
Elite Academy
Career Point
R. S Tutorial Engineers
Study Circle
Brilliant Tutorials
Resonance
Vidyamandir
Mentors Eduserve
Omega Study Center, Muzaffarpur
Vision Classes
Sri Chaitanya
As I mentioned above that you need to check properly before enrolling. Read reviews on the internet and talk with some of the students from the coaching institute and make a well-informed decision.
Best of luck.