Top government college in India for research in physics are as follows -

1. Indian Institute of Technology (IIT), Bombay
2. Indian Institute of Science (IISc) – Bangalore
3. IIT Madras
4. IIT Delhi
5. IIT Kanpur
6. Tata Institute of Fundamental Research (TIFR), Mumbai
7. Delhi University

As most of the colleges are IITs so you have to clear JEE Advanced and for TIFR you have to give their entrance exam TIFR GS and same regarding Delhi University, you have to give DU entrance exam.

Hope it helps!