If you had scored above minimum percentage of 75% in your class 12th, only then you have a chance for lower NIT, you can check previous cutoffs on the following link

https://www.google.com/amp/s/engineering.careers360.com/articles/nits-cutoff-for-top-btech-branches/amp
You can also check for top private universities like Thapar University, Jaypee  NOIDA,.
Also for other available colleges with your rank you can check on our college predictor link provided below
https://engineering.careers360.com/jee-main-college-predictor
Hope this solves your query.