Hey,
The eligibility criteria of JEE Mains include that the candidates should have obtained a minimum of 75% marks in class 12 or equivalent exam or they must be in the top 20 percentile in their class 12 examination. For SC/ ST, the eligibility is to obtain a minimum of 65% marks in class 12 or equivalent.
The top 20 percentile cut off marks is released separately for IITs and other institutes (NITs, IIITs and CFTIs) on the official site of Josaa. So, you are eligible for NITs.
The cutoff changes every year depending upon the number of candidates appearing in the examination,category etcetra. Since your percentile is 96.6, so your approximate rank is 29,546 which is good and you can expect good NITs.
You can use our college Predictor to know about your chances in different colleges:

Hope this helps.
Good luck.

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