Hello Ariba,
I can't tell you the state merit rank up to which you can get admission in a government medical college in Bihar, but yes I can definitely tell you the maximum All India rank up to which you can get admission in any Government medical college in Bihar with unreserved category.

• Anugrah narayan magadh medical college and hospital, gaya- 11235 AIR
  
• Darbhanga medical college- 11250AIR
  
• Government Medical college, bettiah- 11068 AIR
  
• Indira Gandhi institute of medical Sciences, Patna- 10516 AIR
  
• ShriKrishna medical college, Muzzafarpur- 11253 AIR
  

This list is according to the last year's cutoff list.
For more information refer to the following link.
http://www.medicine.careers360.com/articles/neet-cutoff-bihar
I hope this helps.
All the best for the future!!