M.Sc Astronomy

Yes, you can opt for M.Sc. astrophysics after completing B.Sc. in physics, electronics and maths.

Kindly visit the link mentioned below:
https://www.shiksha.com/

Some of the best private institutes for M.Sc in astronomy are as follows:
1) India Institute of Science, Bangalore
2) IUCAA, Pune
3) Punjab University, PU
4) Indian institute of Astrophysics, Bangalore

Hi
Check the following colleges and their course structure:
Indian Institute of Astrophysics, Bengaluru.
Indian Institute of Science, BengaluruBITS, Pilani.
IISER and NISER
Tata Institute of Fundamental Research, Pune.
Osmania University, Hyderabad.
Punjab University, Chandigarh.

Absolutely you can. Check the details at leading institutes like IISC, IISER and IIA.

Hi
There should not be any hindrance in pursuing your master's after the qualification you mentioned. Few of the indian institutes offering this degree are
1. http://www.iiap.res.in/intphd.htm
2. IISC bangalore
3. IISER
4. http://www.pondiuni.edu.in/department/department-astrophysics

Thanks a lot Aneeket and @aditya-kumar
Every institute has their own criteria for admission. However, if you have studied Physics and Mathematics at undergraduate level (B.Sc.) with minimum 45 %, you are eligible for the course. Universities offer the courses as M.Sc. Astronomy or M.Sc. Astrophysics
You may also decide about integrated M.Sc. Ph.D in astrophysics from Indian Institute of Astrophysics
Other options are
Osmania University, Hyderabad
University of Pune
Tata Institute of Fundamental Research Mumbai (Most recommended)
St. Xaviers College Kolkata
@aneeket has also given valuable suggestion above, you must refer them too