Unfortunately JEE Mains cutoff for general cast is 89 percentile this time that means you have not qualified JEE Mains, so it is difficult to get inside a government college in any region to be true.
But still there is hope, there are many low graded government college present which except student even with low ranking in jee mains
You can check out

• Bakhtiyarpur College of Engineering, Patna
  
• Loknayak Jai Prakash Institute of Technology, Chhapra

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