Hey Misha.
The  cut off for most of the government medical colleges in Bihar for admission under the State quota for the SC category was  score of 370 marks and above. Considering this you seem to have a great chance of admission in a government college. But also keep in mind that the cut off changes each year due to several factors like level of difficulty, competition etc. Still a score above 380 would be safe for admission here.
You can use the link below for previous year trends.
https://medicine.careers360.com/articles/neet-cutoff-bihar/amp
Best of luck

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