Dear Jyoti, for SC category, 370 marks got a seat in Government Medical Vollege, Bettiah. The other colleges that have cut offs lesser than your score are:
Anugrah Narayan Magadh Medical College: 380
Jawaharlal Nehru Medical College: 380
Shree Krishna Medical College: 387
Vardhaman Institute of Medical Sciences: 371

Having said that, cut off changes every year and is dependant on various factors like no.of seats available, no.of candidates appearing for the exam, top NEET score and difficulty of the exam.Please visit this link to check previous cut offs to have an idea of your chances at various colleges:
https://medicine.careers360.com/articles/neet-cutoff-bihar/amp

Yes you can get a MBBS seat in a government college with this score under state Quota. Some of your options are,

• Anugrah Narayan Magadh Medical College and Hospital, Gaya
• Darbhanga Medical College, Laheriasarai
• Government Medical College, Bettiah
• Jawaharlal Nehru Medical College, Bhagalpur

You can yourself check previous year cutoffs of colleges of Bihar by going through the given link.

https://medicine.careers360.com/articles/neet-cutoff-bihar

You can also predict what colleges you might get with this rank by going through the link of college predictor tool given below.

https://engineering.careers360.com/jee-main-college-predictor

Hope it helps.

Thank you.

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