Hello Anil, there are a number of government colleges offering aerospace engineering course. Some of the top colleges are: 

1. IIT Madras, 
2. IIT Bombay, 
3. IIST Thiruvananthapuram
4. IIT Kanpur
5. Hindustan Institute of Engineering Technology, Chennai
6. Panjab Engineering College, Chandigarh
7. School of Aviation Science and Technology , Delhi

A List of Top Colleges for Aerospace Engineering in India :

1.Indian Institute of Space Science and Technology, Thiruvananthapuram

2.Indian Institute of Aeronautical Engineering, Dehradun

3.Madras Institute of Technology, Chennai

4. Hindustan Institute of Technology and Science, Chennai

5.Punjab Engineering College, Chandigarh

6. Park College of Engineering and Technology, Coimbatore