Hello student no all the IIT's NIT's and IIIT's are public/government colleges none of them are Private.

Eligibility - Candidates must passed or appearing class 12 in Physics chemistry and Mathematics with minimum 75 percent marks aggregate from a recognized board (this year only passing certificate).

To get admission in NIT's, IIIT's, and IIT's you need to appear in Jee main entrance examination.

Feel free to comment if you've any doubt

Good luck