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Yes I think you can do that. MSc is the course you are talking about I think. You can enroll in that course with a graduation in science degree. But you can also opt for M.Tech. It can help you even better.
Inside India? Theoretically yes, practically no (there are a lot of regulation/administrative problems). You can, however, do this in the USA without facing too much trouble.
#-Link-Snipped-# Engineering Physics is not exactly what is taught in MSc physics, though it is related. India does not have good equivalents to an Engineering Physics degree yet (except for the B.Tech in a few IITs).