Astronomy

https://www.shiksha.com/b-tech/jee-advanced-exam-cutoff
Refer the link.

Hi,
M.Sc cosmology + Ph.D. in Cosmology will complete your goal. Institutes to study cosmology in India Institutes of Space Science and Technology, Trivandrum. Indian Institute of Astrophysics, Bangalore. Tata Institute of Fundamental Research, Pune. Raman Research Institute, Bangalore. Physical Research laboratory, Ahmedabad. Indian Institute of Sciences, Bangalore.

You have done graduation in mechanical engineering and are desirous of doing your PG in different subjects. For PG in a particular subject there is distinct eligibility criteria and one can't pursue PG in unrelated topic. You can download brochure from your prospective institutes webpage for details.

IITs do not offer undergraduate courses on astrophysics.

Please refer to the link mentioned below for details. https://www.shiksha.com/university/indian-institute-of-space-science-and-technology-thiruvananthapuram-25141/admission#admission

Yes, you can.The minimum eligibility required to be MET for admission to the course is graduation completed with Science from a recognised university with a minimum aggregate score of 50%. A few universities and colleges in India conduct entrance examinations for admission to the course.

The course for Astrophysics
Obtain a bachelor's degree in astrophysics.
You will need to take calculus-based physics, computer science, and astronomy. A few electrical engineering classes may also be required. Bachelor's degree programs typically take 4 years to complete.
10 Astronomy Institutes in India that are fostering Space.
Aryabhatta Research Institute of Observational Sciences, Nainital.
Indian Institute of Astrophysics, Bangalore.
Indian Institute of Science Education and Research.
Indian Institute of Space Science and Technology, Thiruvananthapuram.
Inter-University Centre for Astronomy and Astrophysics, (Pune)

It is best to score above 80 percentage to get into such a top rated university. The competition could be tough.