You haven't mentioned the Home State you belong to. Nevertheless, going by previous years data, a percentile of 96.67 ia approximately an All India Rank of 35325 and the chances of you securing a seat in various Colleges are as follows:

NIT Arunachal Pradesh: Chemical Engineering

NIT Sikkim: Biotechnology

NIT Nagaland: ECE

NIT Meghalaya: EEE

Now this is based on 2019 data and cut offs change every year. Cut offs depend on various factors such as total no .of seats available, difficulty of the exam, previous year cut offs, no.of Candidates appearing for the exam and no.of Candidates applying for a course. Please use our College predictor for the complete list of Colleges that you may have a shot at: https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer