Hi

It's quite difficult to predict because cut off  depends upon various factors like

------------) number of students that appeared in the neet exam,

------------) kind of marks obtained by them ,

------------)  toughness level of the neet examination

------------)  number of seats available etc

>>>>>>> with 15697 ews rank

Yes, you can get NIT Trichy under Tamilnadu home state

For example,

In 6th round of josaa counselling 2020,

Under  home state,18752 ews  rank got mechanical engineering in NIT trichy for ews category gender neutral.

You can check the same at

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

This prediction is on the past year data basis but  cut closing rank for colleges changes every year depending upon factors like number of candidates that write jee main examination, difficulty level of the question paper for different shifts of jee main 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

To help you  further,

Minimum percentile in jee main 2021 to qualify it to  be eligible for jee advanced 2021 is given below :-

--------) general :-87.8992241 percentile

--------) EWS:- 66.2214845 percentile

--------) OBC-NCL :- 68.0234447 percentile

--------) SC :- 46.8825338 percentile

--------) ST:- 34.6728999 percentile

--------) PH :- 0.0096375 percentile

Thank you