Hello Monish,

You can take admissions at NITs through JEE paper 2 via 2 quotas, i.e.

1. Home state quota

2. Other state quota

The cutoffs are also different based on category (Open, OBC-NCL, SC, ST)

You can visit the below link to know the trends of opening and closing rank of NITs based on quotas & category

Here you can find the closing rank of NIT Trichy which will clear your doubt.

https://engineering.careers360.com/articles/jee-main-cutoff-for-b-arch-b-planning

Also, you can use the college predictor tool-

https://engineering.careers360.com/jee-main-architecture-college-predictor

Hope this is helpful. Good luck!!