Mining Engineering

Hello Vivek,
Actually all three are unique in their own way. Mechanical has applications in almost every field. Mining too is very important. But my vote is for Automobile. It's going to witness disrupting changes in coming years.

No, it doesn't. It only offers BE in mining, not M.Tech.

The scope is wide in India and abroad, Australia, Canada and countries in the Gulf are some of the best countries in this profession. Major companies in India are Coal India, ONGC and IOCL. You may gain some work experience in your home country before searching a job abroad. If you seek international exposure, you should strongly consider a foreign country. Labour shortage list of the countries will give you an idea of the job scenario.

Mining engineering is good but the scope is very limited. I recommend you to choose & practice profession which has global demand/opportunities/ openings. Not everywhere you get jobs and the demand is comparatively less when compared with other engineering professions. This profession also deals with kind of unhealthy atmosphere (Nowadays, a lot of precautions are taken but still). The payment is pretty decent for this profession because there's a lot of risk factor involved too.
Practice a profession which can support you anywhere, anytime in the world with some ease.
Everyone's perspective may vary but this was my point of view.