Hello,
With such rank it is difficult to get seat in NITs. You need to secure rank below 5,000 to have decent chances of getting seat in a NIT in a desired branch. Considering 2019 cut off it is difficult to get seat, However, you may go for state counselling, there are states which conducts counselling based on JEE Main score such as Haryana, Madhya Pradesh, Uttarakhand etc. You may seek admission through state counselling. Cut off is subjected to change, it may increase or decrease slightly depending on number of candidates appeared, difficulty of exam and number of seats available etc.
We have JEE Main college predictor, you may predict the colleges in which you may get using it https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer
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