Masters

If you wants to go in teaching profession than M.Tech will be the right option because this will enhance your confidence level and teaching skills. Apart from GATE, there are many Institutes offering M.Tech courses through their own entrance exams like GGSIPU, LPU ( GATE and LPUNEST), VIT, SRMIST, BITS Pilani and Mesra, TIET (With and without GATE). Now a days, most of the engineering graduates are preferring for doing the Management courses from some reputed Business schools for availing the best placement opportunities. Hence you can choose anyone from above as per your interest.

Hi,
Each university can have a different set of rules and bylaws for its different courses. This makes its degrees not only valid for application in overseas courses and programs, but also makes them carry much more weight when its students apply for jobs (both in the government as well as private sectors). Good luck.

Nope. There is no exemption. You will have to attempt all the 4 papers.