M.Sc Mathematics

Yes, it is very much required.

Yes, this course is offered by Gujarat University.

Yes, you are eligible to take admission in many institutions. The cut-off for M.Sc. in Mathematics is 50% aggregate. But in some colleges, you have to take an entrence exam. You can check the best colleges near to your location here:
Shiksha. Com.

Unfortunately, since you have done B.Tech in Instrumentation and control engineering, you do not qualify. You need to be a B.Sc in mathematics and computer education, or any other degree that has math and or computer education. But, you can do it now. So, do it if you really want to get into M.Sc Mathematics, and are passionate about it. Another advantage would be that you will be a double graduate.

After completing M.Sc, you can either take a job as a professor or can study further, complete Ph.D and then work as a mathematician and enter in the research field. Many organizations and companies require mathematicians even you can work with the government in the government organisations like ISRO, DRDO.

If you really are into mathematics and want to study further then only you should for M.Sc. And if believe in entering the real world and want to look for a job and earn by yourself then I would say banking and finance is better.

Engineering Mathematics is a branch of applied Mathematics concerning Mathematical methods and techniques that are typically used in engineering and industry. Along with fields like engineering physics and engineering geology, both of which may belong in the wider category engineering Science, engineering Mathematics is an interdisciplinary subject motivated by engineers' needs, both for practical, theoretical and other considerations out with their specialization, and to deal with constraints to be effective in their work.