M.Sc Chemistry

Akhilesh, almost all the private colleges and universities offer M.Sc Chemistry. In some you can also get specialized M.Sc in Chemistry like Biochemistry, Industrial Chemsitry, Pharmaceutical Chemistry and so on which will increase your career prospects.
Most private universities offer good placements and placement assistance to their students. Some even offer scholarships to meritorious students.
Check websites of some good universities for details.
Good luck.

As a chemist, I would recommend the M.Sc in Chemistry because it is more general. Biochemistry is specialised which might narrow down your future career possibilities.

1. University Institute Of Chemical Engineering And Technology
2. Government Medical College And Hospital

If you go with Industrial chemistry you have only few options, if you go with chemistry you will be having a lot of options.

I think M.Sc. will be a better option for you if you do it from a good college or university.
You can Pursue M.Sc. from IIT's or IISC. For Taking Admission in IIT's you have to appear in IIT JAM Entrance Exam for M.Sc.
Click here to prepare for IIT JAM Entrance test - https://scoop.eduncle.com/iit-jam-exam-syllabus
I hope it will help you.
Best of Luck.