Hi Aspirant!

According to previous year cutoffs and trends there is no chance of you to get into any NIT OR IIIT even the minimum closing rank for the GFTIs in ST category is around 4,500 to 5,500 approximatey but your rank is beyond that range so it is impossible to get any seat even in GFTIS  but if you belong to Assam state then there is some chance to get into Assam University based on Home State Quota.

Still you can try your luck by participating in CSAB special round counselling to get seats.

Don't forget to check out the Career360 College Predictor to know your college admission chances based on your JEE Main Rank, Home State, Caste, Gender, etc. - https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Happy Hustling.