Hello,
Astrophysics is an applied course and only a very few colleges offer this course. Its more related to aerospace engineering and astronomy. The colleges that offer this course in India are:
Its not necessary that you should do B.Sc., you can do B.Sc./M.Sc. in Physics and do PhD. There is one year course in IISc after M.Sc./B.Tech/B.E to join PhD. PhDs are given in TIFR, Raman Reserach Institute, Institute of Mathematic Sciences. You should have strong foundation in quantum mechanics, maths, classical physics.
For more details you can visit https://www.iiap.res.in/?q=opportunities/career
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