Bihar

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.

First you should decide what you want to do: BA or appear for the UPSC exams. If you are aiming to do BA economics you should try and score high marks in your 10+2 level examinations so that you are eligible to gain admission in BA economics in a college of your choice.
If you are interested in the civil services, you should devote yourself to studying for the UPSC exams,as this is no mean task. You will have to study at least 8-10 hours a day depending on your capacity to grasp different topics.
So basically, you should first sit down and decide which course or exam you want to give. You could also take the help of a career counselor to help you decide on a favorable course.