M.Sc

Yes, definitely, you can do it. But rather, try for MD Biochemistry where you will get more wider prospective in teaching Biochemistry. All the best.

Please click the link below for all the details related to pattern and syllabus for the entrance exam of M.Sc
https://www.shiksha.com/science/articles/how-to-prepare-for-top-msc-entrance-exams-blogId-13489

Below are the colleges that offers integrated M.Sc. And Ph.D. course for biological Science:
1. NISER
2. NMIMS University
3. NCBS.

It is Integrated M.Sc-Ph.D programme taht NISER offers. For more details, click below
http://www.niser.ac.in/sps/ug-core-courses
http://www.niser.ac.in/sps/sites/default/files/pdf/NISER_SPS_Integrated_PhD_programme.pdf.

Hello,
After completing B.Sc. Chemistry, there are following well known M.Sc. Entrance exams :-
1) IIT JAM exam
2) TIFR GS TATA Institute of Fundamental Research) exam
3) BITSAT
& any other universities like Pune University.

One of the well known colleges is Symbiosis School of Biomedical Sciences. They offer two year full-time M.Sc in Biotechnology. Any graduate with 50% marks can apply for this course. One of my friends studied here and now he is doing his Ph.D. Here you'll get practical as well as thorough subject knowledge.

Hello,
For M.Sc Entrance exams, you have to clear all basic concepts regarding particular subject.
Go through class 11th, class 12, FY, SY, TY B.Sc books.

You are not eligible for M.Sc in Chemistry. You can do M.Tech. /ME in Chemical engineering. If you want to M.Sc in maths, then you are eligible because it is necessary to study the subject at least for 2 years/4semesters in which you want to do Master's degree. In B.Tech Mechanical, a student studies Maths in 2 years but, he studies chemistry only for 1 year /1 semester.