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These are the major ways in India for doing Msc or integrated Ph.D.(or direct Ph.D. in some cases) in physics after engineering. [Note: Details about Distance MSc physics degree for B.E/B.Tech holders are at the bottom part of the post.]
Opportunities abroad (Physics GRE, General GRE, IELTS and TOFEL etc)
TIFR GS(Integrated Ph.D. paper)
University entrance tests.
MS by research programs
You can check details about exams in this page Exam and Probable Dates
The three exams JEST, GATE, and NET have syllabus of Msc+Bsc. All other mentioned above are conducted on Bsc level syllabus and are easier for us Engineers(B.Tech or B.E) with less physics background to crack.
JAM exam: This is conducted by IITs as an entrance test to Msc and integrated Ph.D. in IITs and IISC. Also, some IISERs take jam rankers to integrated Ph.D. This is the best of all options for slow learners. For those who can't spend a year preparing for entrance tests, this will be a boon. Even if you prepare perfectly only up to 12th class level physics, you can get a rank under 500 easily. So, even if you are preparing for JEST, I strongly recommend keeping this as a backup option at least.
Caution: IITs and IISERs ask for 2 years of physics related subjects in bachelors as compulsory for JAM rankers. I heard that mechanical guys may not meet these criteria. To confirm if you will meet the eligibility criteria, mail those institutes and inquire. I think IIT Kanpur and Bombay give an exception.
TIFR GS: TIFR is one of the elite research institutes in India if not the best. Even better than IISC as far as physics is concerned. If you opt for integrated Ph.D. paper, Your questions will be from Bsc syllabus but the no.of questions will be less and look for your deep understanding of a concept. Very few people get selected this way. The interviews will also be very thought-provoking. You need to be very strong with your fundamentals. All TIFR institutes will take students through this.
Opportunities Abroad (Physics GRE, General GRE, IELTS and TOFEL etc): I personally feel if you can fund yourself, then this is the best of all the options mentioned. Because switching career is very easy thing abroad and the opportunities you have there are numerous and the research happening even in the mediocre colleges there is comparable to good colleges here. General GRE with a combination of TOFEL or IELTS is necessary for the USA and Physics GRE is recommended. As for the European countries, only IELTS is enough (Sending GRE scores might add to your profile but is not mandatory). The tuition fee is zero in some countries like Italy and Germany.
Refer to this answer for Physics GRE preparation
Physics GRE Discussion Forums this might be helpful
TIFR Hyderabad: If you have a score above 480 GATE score in any stream you can apply for this. This is a program designed specifically for interdisciplinary and B.tech graduates. It may definitely not be as good as the main campus of TIFR but still, it is one of the very good institutes in India.
Universities entrance tests: I've strenuously searched eligibility criteria of at least a 50 to 100 major colleges and universities and of all those, some of which I found to give admits to B.tech grads in Msc physics are
JNU ( application starts in early September itself be watchful)
IUCAA INAT exam (even this application comes out in September )
University of Hyderabad
The Central University of Haryana and Central University of Rajasthan ( they have a common entrance test CUCET. I'm not sure how good these two institutes are..do your own research)
MS by research: some institutes and IITs offer MS by research programmes. IISER Kolkatta offers one in space research. If you happen to be interested in that specific field of research then it would be a boon to you.
JEST: It is an exam conducted on Msc level syllabus and is accepted by almost all elite research institutes (check the JEST website) A good rank in JEST can get you into research-oriented institutes which JAM can’t offer.
The reason I have put JEST so low on the list despite it being accepted in research institutes is:
All most all of the institutes(HRI is the only exception I know of) that take through jest, offer integrated Ph.D. only. It’s not suggested to leave in the middle with a Master degree. If you have any dreams of going abroad or to go to better institutes, you can’t achieve them. But if you do MSc or Ms through JAM or other good Universities and build up your profile, You can pursue Ph.D. in much better institutes in India or abroad. But keep in mind that MSc in IITs may not give you research experience as much as these research institutes do.
Its syllabus is vast and some may feel difficulty in cracking it with one-year preparation (not impossible though). I personally do know people who cracked JEST with 1-year preparation.
GATE and NET: B.tech/B.E grads are eligible to write GATE and NET but they are not quite relevant for engineers looking to do M.sc.
Other exams for some institutes like CMI also accept B.Tech/B.E grads for both integrated and direct Ph.D., check their websites and also ensure you meet all their eligibility criteria.
You may also refer this answer for some more information
For those who are working and can't afford to leave the job to prepare for exams, this will be a boon.
From what I've heard, many engineers start teaching in some coaching institute for 12th class or JEE and parallelly do MSc in distance. This way you'd be earning, doing masters and most importantly you'll be working in a physics-related field and so your basics in physics will be strong. But again I'm not sure if the non-regular nature this degree might affect your chances of getting Ph.D. While I believe the elite institutes do not bother much about your educational background, all that matters is your interview, I'm still ambivalent about this. If any reader could collect information regarding this and share it with us, it'd be really useful.
These are the open universities that I know of to give admission to MSc Physics course for Engineering Grads:
Vardhaman Mahaveer Open University (Link)
also, check about the validity of those degrees.