Hello. Not all universities are under government. Some universities which are self established are the private universities and they do not come under any government.

I am listing some universities,  kindly check it.

1) Amity university

2) LPU

3) Manipal

4) VIT

5) BITS

6) UPES

7) SRM

8) Chitkara university

9) Nirma university

Careers360 article will help you know which universities are under government.

https://university.careers360.com/colleges/list-of-government-universities-in-india

Hope that helps!