Hello, IITs and IIMs are public-run autonomous institutions, i.e the Government Funds them.

The Indian Institutes of Technology ( IITs ) and Indian Institutes of Management ( IIMs )  are autonomous public technical universities located across India. It is under the jurisdiction of Ministry of Education, Government of India. They are governed by the Institutes of Technology Act, 1961, which has declared them as Institutes of National Importance and lays down their powers, duties, and framework for governance