Hi Vushak,

First of all, since you have just passed tenth, take up pure science. If you are able to cope with it, as some students are not able to, then after completing 12th opt for an Honours graduation degree course in Physics under a reputed university.

When you are in the 3rd year of that course, there are several exams like JAM, JEST, TIFR etc. Several institutes that teach astrophysics, astronomy and cosmology take the score of these exams into account(for example, Indian Institute of Astrophysics, Bangalore; Saha Institute of Nuclear Physics, Calcutta and many more). Once you crack any of these exams. Bingo! You would be doing Integrated Ph.D. in astrophysics at any of these institutions.

You can also opt for another method.
After completing graduation, you can do post graduation and then give these exams to enroll you for a Ph.D. at a reputed institute.

Good Luck!