The closing ranks generally vary every year depending on number of studenst appeared, difficulty level, previous year cutoff trends.

So difficult to gauge any minimum score, but as per trends the  cutoff to get into newer  NITs is  under rank 40,000 under JEE mains as NITs accept only JEE Mains.hence, suggested score of more than 150+ is safe to be considered for getting newer NITs while for top NITs a minimum of 210+ is must.

Https://engineering.careers360.com/articles/jee-advanced-cutoff

Coming to top IITs, the cutoffsare under rank 2000 and with newer IITs the cutoff ranks under 9000, which results into cutoffof 310+ for top IITs and for newer IITs it should be around 185+.