Physics Spl

Hello Govind,
Yes, you can. Most universities require you to have physics as your extra-departmental/pass course for you to study physics in M.Sc. However, since science departments offer admission to Master's degree students via entrance exams, this might be difficult anyway. You'll have to work hard in physics to crack entrance exams. Alternatively, you could apply for an applied mathematics degree in Calcutta University or CMI or even for M.Sc in mathematics. Most of the departments have someone or the other working in the mathematical physics. Courses that are relevant to that are differential geometry, probability theory/functional analysis, representation theory/Lie groups and of course, the theory of differential equations.
Approaching physics via mathematics is reasonably common.

What you need is a sufficiently concrete goal, that will organise your course of action from now on. I suggest that you try & aim to do a PhD in the US in one of the top 10 (or 20 or 30) universities, in a subfield of physics that you like.
Be warned that the path towards that is not entirely clear. But it is a good organizing goal because it will force you to think, decide & act with some focus instead of treading water & doing aimless things. This focus is extremely valuable. The trouble is that US universities require a four-year undergraduate degree before applying for Ph.D, & most of the Indian universities only offer Bachelor's degrees which are of 3-years. So you can either do Bachelors & Masters & then apply, or you can do engineering, physics or something of the kind from an IIT & then apply. In my case, what I did was to do a B.Tech from IITM in electronics (this was possibly a mistake, but it worked out, fortunately) & then switch over to physics when applying for Ph.D in physics. If you have a good resume, recommendation letters, good GRE scores etc US universities are pretty flexible about switching fields. Here is an answer I wrote before on a loosely related question, maybe that will help.
To the wounded patriots who might get offended by my suggestion to not do Ph.D in India: I don't doubt that India has a competent theoretical physics community at this time, we seem to have attained critical mass in the last few decades, & we do have some first rate physicists here. But competence/excellence etc. are only part of the criterion in deciding where you do your Ph.D. Doing a Ph.D abroad expands your brain like very few other things do, in my experience. So I highly recommend it.
Most importantly, don't make too many inflexible decisions too early (like "I will only study/work in India", "I will/will not work on this topic", etc) before you have had the knowledge & experience & wisdom to decide for yourself. This takes time, so form judgments & act on them, but be willing to change your previous decisions if you find they were wrong, instead of stubbornly sticking to them. Stubbornness is a resource and should be used with extreme caution. For example, I started out thinking that string theory was too speculative but ended up becoming a practitioner over time. As I learned the subject, I slowly realized that I simply wasn't qualified to have the early judgments I had about the subject. Of course, one could say that this is the process of info.