Hello Aspirant,
On such rank and category you have very low chances of getting any government medical colleges under AIQ counselling according to previous year's cut-off. As we go through previous year's cut-off then it shows that last year the closing rank was around 80,000 for All India quota counselling for ST category. But yes you can try for government colleges through state quota counselling of your respective state.
You can check out previous year's cut-offs from the link given below :-
https://medicine.careers360.com/articles/neet-cut-off-for-government-colleges
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 because it will make you comfortable while choice filling in counselling :-
https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer
I hope this information helps you.
Good Luck!!
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