M.Sc

Hello Gourav,
The link below gives the list of colleges for M.Sc mathematics in Tamil Nadu:
https://www.shiksha.com/science/colleges/m-sc-mathematics-colleges-tamil-nadu

Yes, why not. There are many fields in physics. You can go for research.

Mathematics is a better option, as it is helpful in your Bank Examination. Math is a key to your success.

Ashish, I think you can as eligibility talks of allied as well as applied science too. Nursing is part of allied science.
Many good universities like LPU, GNA, CU, etc are offering the course. All these universities have wonderful infrastructure and world-class facilities to offer to students apart from good placements that they offer. Some like LPU also offer wonderful scholarships for making quality education affordable for all.
Good luck.

Simran,
You have some good private universities around you like Lovely Professional University, GNA, etc where you can try for admission. In fact LPU, has very good placement record.
Check with your desired institute for more details.
Good luck.

Students passing B.Sc. Three year Degree Course Examination and having secured a minimum of 50% marks in aggregate will be eligible for admission in M.Sc. Physics Course.

I think you go for M.Sc Industrial Chemistry. Industrial chemistry is a chemistry which applies physical and chemical processes toward the transformation of raw materials into products.The course provided details knowledge in topics such as Heterocyclic, Electrochemistry, Radioactive Elements and Medicinal Chemistry.
Placements of industrial chemistry is very good. There are many colleges which offer m.s.c industrial chemistry course :
IIT Kharagpur
JNTU
Mahatma Gandhi Institute of Applied Science

BFIT Group of Institutions | Dehradun
Himgiri Zee University | Dehradun
This are the only two colleges.