Hello Aspirant, as per your question i have collected a few reputed names. They are as follows:

1) Indian Institute of Astrophysics, Banglore
2) Tata institute of fundamental research, Pune
3) Osmania university
4) JNU, Delhi
5) JNTU, Hyderabad

I hope this information was useful for you.

Hello Praseep 

You can pursue astrophysics in BSc too. 

List of colleges which offer BSc Astrophysics course in India.

1.Indian Institute of Science, Bangalore

2.Institute of Fundamental Research, Tamil Nadu

3.jntu College of Engineering, Hyderabad

4.Astrophysics, Tata Institute of Fundamental Research, Pune.

5.Osmania University

6.Birla Institute of Technology & Sciences, Pilani

7.Institute of Fundamental Research, Tamil Nadu

8.Andhra University

9.Raman Research Institute, Bangalore

10.Birla Institute of Technology & Sciences, Pilani