M.Tech. (Research) in Electronic Systems Engineering 

at Division of Electrical, Electronics, and Computer Science (EECS), CV Raman Road

Yes, Electronics Engineers are also recruited by the DRDO. The organisation releases notification in case of any requirement or vacancy in the pertinent discipline. The recruitement to DRDO is done on the basis of an open-recruitment process which attracts the brightest minds and experienced candidates from the country. 

The Electronics Engineering syllabus for the BTech degree is not the same across all colleges. Every college prefers to follow an individual coursework module that includes both theory classes and practical lab work. While core subjects and fundamental concepts might be similar, the structure, electives offered, and laboratory and project work are different.

You can check the detailed syllabus for the course on the respective college websites that you're targeting to get a clearer picture.

Many PSUs conduct direct recruitment on the basis of marks scored in GATE instead of conducting their own separate recruitment examiantion. Electronics Engineer will also be required to qualify GATE in order to secure a job in PSUs. After qualifying for the exam with good marks, students may get a job in PSUs. 

Yes, Candidates who wish to become a professor after BTech in Electrical Engineering will also be required to complete MTech and PhD in the required discipline.They must clear GATE in order to pursue M.Tech and later pursue PhD in the same discipline. They must demonstrate excellent research skills by grabbing fellowships and submitting research papers across SCOPUS indexed journals.