Hi there,
Hope you are doing well.
With OBC-NCL Category and Tamil Nadu as home state, you can get some branches in NIT Trichy but its' not clear as what is your category rank exactly.
So, here is the list of branches with closing rank for OBC-NCL:-
1) Chemical Engineering:-5225
2) Production ENgineering:-7330
3) Metallurgical and Materials Engineering:-7719
4) Civil Engineering:-8441

Hope it would help.
Thank You.
Check out our JEE Mains College predictor to see your probable Chances for different branches in different NITs and GFTIs:-
https://engineering.careers360.com/jee-main-college-predictor

hello

going by the previous year trends you can get metallurgy at nit trichy if you have home state quota. you can check this using the careers 360 jee main college predictor at https://engineering.careers360.com/jee-main-college-predictor.

hope it helps.