Hello,

I must tell you, if you are talking about engineering centralised counselling, then No you are eligible for Home state only from the state from where you have passed Std XII which in your case is Bihar only. 

Considering NEET counselling, there is a provision of that, and in NEET MP counselling, if you have domicile certificate you are eligible for the counselling process and can get seat via it easily. I hope it helps.