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Hello Aspirant,
Based on your score , your overall predicted rank would be 52192 - 64342 Cutoffs vary with factors like the total number of seats available, number of students competing, the difficulty level of the exam etc. Hence it difficult to predict for sure but based on the previous year cutoff trend the expected range of marks for BC category for government colleges in TN would be minimum 480-500+ , for top ranked ones it can go up to 580-590+ due to this years competition and for private it would be 430-450+ may be fine. The BC cutoff does not differ much from general cutoffs. So go through the below article to see previous year college wise cutoffs:
https://medicine.careers360.com/articles/neet-cutoff-tamil-nadu
Only when you attend the counselling you will know the exact scenario. Anyways you do have a fair chance.
Or use the college predictor tool to know your options:
https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer
All the best
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