Mechanical Engineering have so many sub-branches like Aeronautical, Automobile, Thermal, Robotics, Materials Science etc. even bio-tech is also a sub branch of ME. Actually, all these courses will be there in your masters but nowadays people are including these branches in bachelors. Mechanical engineering is the mother of all these branches. So, you can do M.Tech in aeronautical. The subject will be full of the basic courses like Fluid mechanics, Heat transfer, Thermodynamics, FEA and you should be good in calculus.

If you want to do it in IIT’s then opt for GATE, my suggestion do M.S