Hi

With 96.6 percentile

• Your rank will be  around 34782 - 39100  as per our rank predictor at

  JEE Main Rank Predictor 2021 - Predict your JEE Main ...

  JEE Main Rank Predictor - Know your expected IIT JEE Main 2021 Rank by ...

Your ews rank will be around 5000.

With this rank yes you do have chances in NIT . ( Haa, aapko NIT mil sakta hai )

For example,

In 6th round of josaa counselling 2020, under other state quota  6987 ews rank  was closing rank for gender neutral for ews category in NIT Patna  for civil engineering

You can check the same at

https://josaa.nic.in/Result/Result/currentorcr.aspx

Above prediction is on the basis of past year data but  cut off/closing rank for colleges keeps changing every year depending upon many factors like number of students that appeared in the examination, difficulty level of the JEE main question paper for different shifts etc so

To have a personalised report on your chances of getting a college you can go through our college predictor, it will give you complete list of colleges which you can get on the basis of the category you belong to,  your home state, your gender etc, the link for  jee main college predictor is provided below

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

If you have any other doubt then you can always reach us to clear them :) we are always available to help you out and guide you

Thankyou