Hello Aspirant,
On such rank and category you have good chances of getting management quota seat in some Private medical colleges in Tamil Nadu under state quota according to previous year's cut-off. As we go through previous year's cut-off then it shows that you can get following colleges :-
And some more. You can check out previous year's cut-offs from the link given below :-
https://medicine.careers360.com/articles/neet-cutoff-tamil-nadu
Note that the above prediction is made on the basis of previous year's cut-off and the cut-offs are bound to change every year depending upon various factors such as the number of candidates appearing in an examination, the number of candidates qualifying an examination, difficulty level of the paper, and so on.
To have a list of all those colleges which you can get based upon your marks, category, and state you can use NEET College Predictor:-
https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer
I hope this information helps you.
Good Luck!!
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