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Hello Aspirant,
On such ST rank you have no chances to get any of the NITs even after considering your home state because as per the last year data the closing ST rank was somewhere around 3-3.5k and you are very far from the figure.
You can check out previous year's cut-offs from the official website of JOSAA as given below :-
https://josaa.nic.in/Result/Result/currentorcr.aspx
Note that the above prediction is made on the basis of latest cut-offs available on official website of JOSAA or CSAB 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 JEE-Main College Predictor:-
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
Now if you appeared for JEE-Advance 2021 then you must have got your result so to have a list of all those colleges which you can get based upon JEE-Advance 2021 score you can use JEE-Advance College Predictor:-
https://engineering.careers360.com/jee-advanced-college-predictor?icn=QnA&ici=qna_answer
JEE-Advance 2021 cut-offs are mentioned below :-
>>> Common rank list (CRL) - 10.0 (Minimum percentage of marks in each subject) - 35.0 (Minimum percentage of aggregate marks)
>>> GEN-EWS rank list - 9.0 - 31.5
>>> OBC-NCL rank list - 9.0 - 31.5
>>> SC rank list - 5.0 - 17.5
>>> ST rank list - 5.0 - 17.5
>>> CRL-PwD rank list - 5.0 - 17.5
>>> GEN-EWS-PwD rank list - 5.0 - 17.5
>>> OBC-NCL-PwD rank list - 5.0 - 17.5
>>> SC-PwD rank list - 5.0 - 17.5
>>> ST-PwD rank list - 5.0 - 17.5
>>> Preparatory course rank lists - 2.5 - 8.75
Now if you are not in the race of JEE-Advance then I would recommend you to either go for private colleges or you can prepare for further attempts of JEE-Main and to help you in your preparation we have some resources which you can access from the link given below :-
https://learn.careers360.com/jee-main-coaching/?utm_source=%20QnA
I hope this information helps you.
Good Luck for your future!!
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