Yes you can get a seat in nit trichy through dasa category . You can give sat and apply for it . It will be certainly easier than jee and also competition will be less.

Please follow the link mentioned to get detailed information about the courses and number of NRI students they allow for admission in different nits

https://www.google.com/amp/s/studyabroad.careers360.com/articles/top-engineering-choices-for-nricwig-in-nits-iiits/amp