Hey Aspirant,

This is possible.For admission to foreign institutes you have to give gre(graduate record test).Admission to indian institutes is through GATE(Graduate aptitude test).

There's no need to do that.
You have already got a B.Tech as well as M.Tech degree after completing the 5 year integrated M.Tech course. So doing M.Tech again is Like doing an M.Tech course of 3 years. Instead, go for PhD, if you are interested in Research.
You can even try giving Indian Engineering Services (IES) Exam, to get a job in the government sector.