Hello.
You have good chances to have NIT with 96 percentile but it depends on your rank it is difficult to predict your exact rank but you can calculate your approximate rank by using the below formula:
((100-your percentile score) X total number of candidates appeared for the exam)/100
Total number of candidates appeared for the January exam: 869010
You can consider for April exam total number of candidates appeared will increase to 12,00000
Now by using the above formula your approximate rank at your mentioned percentile would be: 34,760
(If you do not consider any category wise rank)
Now you can simply match your approximate rank with the cutoff rank of any NIT in any particular branch from the previous year cutoff list of JEE mains to the below link which can give you a probable idea of getting admission.
https://engineering.careers360.com/articles/jee-main-cutoff
Or you can predict your college by using career 360 college predictor tool from the below link.

Best of luck.

IIIT Bangalore

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