Science

By doing B.Sc in any of the courses of pure science, you can't guarantee yourself a stable future in today's world as the value of the degree is not much. But after your B.Sc., you can do your M.Sc, M.Phil and Ph.D. You can end up being a college lecturer or a research scientist.
If you develop any projects then you can have your own start-up and transform it into a big business. So, you have a mammoth number of options.
Hope this helped.

Yes, Physics, Maths and Chemistry is compulsory if you want to do B.Sc (Hons) in physics. There might be some colleges in which it might not be required but in most of the colleges and universities it is an important criteria for admission. So, you have to do your own research in that case.
Hope this helped.

Hi Sheetal,
Eligibility for M.Sc in food and nutrition in Periyar University: Candidate who has completed B.Sc in Nutrition and Dietetics / B.Sc. Home Science / B. Sc. Catering / B.Sc. with PG Diploma in Nutrition and Dietetics / Food Processing, B.Tech. / B.Sc. Food Technology, B.Sc. Life Science courses (Biotechnology / Microbiology / Biochemistry), UG Degree in Allied Health Science (B.Pharm), B.Voc (Food Science and Nutrition related disciplines) and Nursing from a recognised university.

You can choose:
Pharmacy
Biochemistry
Genetic engineering
Microbiology
Chemical engineering
Pathology
Radiology
Environmental biology.