First of all You Don't need to go for GATE or IITies. To become an awesome data scientist or a ML expert, you might need in-depth knowledge of machine learning, artificial intelligence, parallel computing in clusters, and a good deal of core statistics.
These are very specific areas and its a fraction of the syllabi covered in ME / MTech. Also, the depth that is required to work at the cutting edge of these domains are not provided in the masters level. You might have to pursue a Ph.D to gain true expertise in these areas.
One more thing, data scientists need to ask the right questions and formulate the right hypothesis to prove or disprove, apart from making it easily digestible for other departments of a company. The business sense and the communication skills are extremely important - you will not get that in academics.
So my suggestion is take some focussed MOOCs like Andrew NG's Machine Learning course on Coursera to begin with, do small projects by making use of Python's data science libraries, participate in Kaggle competitions, learn R, learn some core statistics.
If you are interested in data engineering, learn the big data tools like Hadoop, Mapreduce, Pig, Hive, etc.
No MTech course in India will make you industry ready. So invest your own time in building right skillset besides doing your day job, and then look for the right opportunities in data science.
Good Luck!!!
