I have done Bachelors in Computer Science, Masters in Political Science and B.Ed in Political Science. Am I eligible for 2nd grade teacher?

Yes, you may be eligible to become a teacher if you have a Bachelor's degree in Computer Science, a Master's degree in Political Science, and a B.Ed in Political Science: 

Eligibility criteria

To become a Trained Graduate Teacher (TGT) in India, you must meet the following criteria:

Pass 12th standard

If you are talking about bihar +2 grade teacher then yes, you are definitly eligible to appear in the bpsc exam and crack to be a bpsc teacher.There is no need of B.Ed be it any subject if you wan't to computer teacher or have done B.Tech in computer scinece.Else based on B.Ed subject Educational Qu