B.Tech

You can apply for TAPMI PGDM & PGDM-HR programs. IMI New Delhi, FORE New Delhi, Great lakes Chennai, Gurgaon, Sri balaji university, Bangalore.

It is a very low CAT score and you may face difficulties in admission. As you have a decent academic profile and with a decent CAT score around 75 to 85 percentile will get into a top B-school.

Yes absolutely maths is required. It is the base of B.Tech. You have to study maths at least 3 semester in CS branch.

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)

You need to have 60% marks in B.Tech and 60 % marks in physics, math & in aggregate. Also, there is an age requirement.

Eligibility: The aspirants of Master's Degree in Hospital Management should possess a Bachelor's Degree (in 10+2+3 form) in any discipline (Except Fine Arts and Oriental Languages) from a recognized university with a minimum of 50% marks. The selection is based on the marks secured in entrance examination conducted.

In India, all the B.Tech courses are offline and within the campus. No distance learning is provided in B.Tech technical.

Correspondance course in B.Tech is not recognised by government of India. So, you wouldn't be eligible for government or may be for private jobs in India.

Correspondence course in BE or BTech is not recognized by the Indian government. So, you can't apply for government jobs in the future.