M.Sc

Your M.Sc subject will depend on which subject you have completed your B.Sc course. Different college are best for different M.Sc course.

Yes, a B.Sc microbiology student is eligible for M.Sc in food nutrition and dietitians from Nirmala Niketan College of Home Science.
Basic eligibility is that Candidate must be a graduate from recognized university. Admission is based on marks obtained in graduation. Regards.

Admission to an integrated M.Sc+B.Ed course is mostly via entrance exam. Few colleges provide admission via direct mode or based on merit I. e marks acquired in Graduation, while others prefer to conduct an entrance exam for entry to their integrated course. Different entrance exams which can be used for entry to integrated M.Sc+B.Ed course are mentioned below:
1) IIT JAM
2) AUCET
3) CUCET
4) NEST
5) KU PGCET
Regards.

Once you complete your B.Tech you should be eligible for studying MS abroad. The basic pre-requisite for an MS abroad is minimum 15 years of formal education, and in some cases, 16 years of education. You may have to appear for the GRE and appear for a few language proficiency tests, like IELTS and TOEFL, if required. Admission process for a course in MS is lengthy and there are lots of pre-requisites to get into top institutes. Please visit college web site individually for complete information, or specify a particular college which you want to study with, so that I may be able to populate relevant details. Regards.

Please refer to the links provided below for an exhaustive list of colleges which offer M.Sc. Physics from Telangana and Andhra Pradesh. You should be able to navigate to a college of your choice using the filters on the web page. Telangana: https://www.shiksha.com/science/colleges/m-sc-physics-colleges-Telangana
Andhra Pradesh: https://www.shiksha.com/science/colleges/m-sc-physics-colleges-andhra-pradesh.

Yes, it is possible to study M.Sc via distance mode after completing B.Sc. To study via distance, you should apply to the college you are interested in studying with, and then take it from there. You might have to furnish some documents as proof of identity and your SSC HSC, and UG certificates, if required. Regards.