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Hello,
As you have mentioned that your neet score 340 marks and you fall under OBC category which have almost same cutoff as that of general category candidates. If we look over previous year's cutoff trend for BHMS / BAMS then, in 2018 402 marks secured a seat for BAMS under 15% All India Quota . And 368 marks secured a seat under 85% state quota.
Now, looking this scenario your chances to get a government seat for BHMS / BAMS is moderate if you apply under state quota.
I hope this would help you. For further queries please feel free to write me down in the comment box.
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