M.Tech

You need minimum 80% in UG to get admission. You need IELTS 6.5 overall and minimum 6 in all component. You also need German language certificate.

You can check the various details of the exam at
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/engineering/exams/amp/vitmee&ved=2ahUKEwik24P1-rzcAhXPXysKHVByBMkQFjAAegQIBBAB&usg=AOvVaw2zr76zcdDuNwdav0rreHDx&cf=1

You can give GATE in any stream irrespective of your branch, but will only get an M.Tech admission in that particular branch in which you have written your gate. But, you will not get a job in PSUS, because in PSUS, if you want to get a job as mechanical engineer you need to have a degree in mechanical engineering itself. So, if you are writing GATE in mechanical engineering to get a job as mechanical engineer in PSUS, then please don't do that, because you are not going to get that by any ways.

To get admission, you need to appear for TANCET.

Your profile says you are a student of B.Tech. If you are asking for a friend, It is not possible to do Engineering after Non-Engineering UG course. M.Tech after BCA is not possible.

Yes, you can get admission for M.Tech without GATE exam.

No, you can't take admission for M.Tech after B.Sc. You will get admission in direct second year of B.Tech, then after you can go for M.Tech. For M.Tech, BE or B.Tech is must to take admission.

M.Tech in Industrial Safety and Hazards Management or M.Tech in safety and fire engineering will be the best options for you
Colleges:
https://www.shiksha.com/engineering/course/m-tech-in-industrial-safety-and-hazards-management-college-of-engineering-anna-university-ceg-guindy-guindy-Chennai-271685
https://www.shiksha.com/engineering/course/m-tech-in-industrial-safety-and-engineering-arulmurugan-college-of-engineering-karur-292245
https://www.shiksha.com/engineering/course/m-tech-in-industrial-safety-engineering-kalasalingam-academy-of-research-and-higher-education-virudhunagar-188975.

Check out the college / course reviews below:
https://www.shiksha.com/college/rvr-and-jc-college-of-engineering-guntur-19405/reviews?course=237386&sort_by=year of gradution&type=question
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