Dear Aryan, last year cut off for most of the colleges lied between 530-540, so you have pretty much higher chances for getting a seat in GOVT college.
Only Patna Medical College had the cut off greater than your score - 552.
Here's the list of colleges -

• Anugrah Narayan Magadh Medical College, Gaya-533
  
• Darbhanga Medical College, Laheriasarai-533
  
• Goverment Medical College, Bettiah-534
  
• Indira Gandhi Institute of Medical Sciences, Patna-536
  
• Jawaharlal Nehru Medical College, Bhagalpur-535
  
• Nalanda Medical College, Patna-537
  
• Sri Krishna Medical College, Mazaffarpur-533
  
• Vardhman Institute of Medical Sciences, Nalanda-534
  

Also, the cut offs are expected to increase this year as the exam was but easy. You can wait for the exact cut off.
All the best.
Feel free to ask for any query.

Hi
As per your query I would like to tell you that you have fair chances of getting a seat in government medical college as last year least marks to secure a seat was 533 marks in
anugrah Narayan magadh medical college and hospital,Gaya
Darbhanga Medical college,leheriasarai
Shri Krishna medical college,muzzafarpur
From your category under state quota talking of which remember that cutoff varies every year depending on number of students appearing in exam, difficulty level of exam, students scoring more than you and your category.
To know more about cutoff of various colleges in Bihar click below
https://www.google.com/amp/s/medicine.careers360.com/articles/neet-cutoff-bihar/amp
Hope this helps

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