B.Sc

B.Tech is better than B.Sc. in IT.

B.Sc. in home science has different fields of specialization like human development, food and nutrition, human resource management, textile and clothing. Each area is unique and anyone can work in wide areas like NGO, school, hotels, as counselors, researchers, etc. As far as Delhi, you need to find out from internet and where Mumbai is concerned, Mumbai University and SNDT University offers home science.

Yes, you can pursue M.Sc in astrophysics but only in theoretical astronomy. For others, engineering is required to pursue higher studies in this. You can refer to below article for this.
http://indiaeducationdiary.in/career-options/Science-Astrophysics-Eligibility.asp

What kind of course you are looking for?

Some universities do allow you to do this, so if you don't get into one program you have the chance to get into the 2nd one.
You need to get in touch with the college for more details.

Among your choices, my recommendation will be as follows: M.Sc. in CS or IT, MBA and MSW. You are advised to choose the subject for your PG based on your interests to excel in your chosen career.