Electronics and Communication Engineering

IIT JAM is an exam for B.Sc student mostly, but there are a few engineering students every year who take a turn and move in this direction. Now, benefits of IIT JAM are:
IIT
Mathematics (as you can't get Physics and Chemistry being an engineering Graduate). Lower competition than GATE, but again it's a new arena for an engineering student for odds aren't the real problem, and the most important, even if it's tough, a Bachelors in Engineering especially non-core like ECE/CSE with Masters in Mathematics is a rare and deadly combination for academic and industrial requirements. I myself is on the same boat, and therefore I know the feeling and I did some research and these are a few of the things I found. One more thing, you should have studied mathematics, any form for at least 4 semesters to get into IITs (most of the courses), just make sure your university curriculum have that.

In NIT Patna both branches are good but CSE is better on the basis of placement, now it depends on your interest.
In B.tech CSE approximately, there is a 100% placement of CSE students. The placements of other branches are quite low. The highest package offered was 39.5 lacs per annum gave to a CSE student by Adobe, and five students were placed for 27 lacs per annum package in Amazon. Companies like Amazon, Microsoft, Wipro, Infosys, samsung, Tata Motors, etc., visited college. The college has a placement cell and the lowest package offered is 3.4 lakhs per annum and the average is 5.68 lakhs per annum. The Wi-Fi facility is available on the campus. The labs are good.
In B.Tech ECE : The average salary package is between 8 to 9 LPA. They provide a good training and placement cell in the college with well-experienced persons. When it comes to the electronics department, placements are somewhat low as compared to CSE.