I would like to know about the relationship between Mechanical and Aeronautical Engineering. Will it be possible to pursue Aeronautical Engineering as PG degree after doing Mechanical Engineering UG degree? How is the demand for such aeronautical engineers in the design field when compared to those who have done the UG degree also in Aeronautical Engineering ?

Well of course, you can pursue Aeronautical as PG degree being UG in Mechanical. It's a good choice though. If you check out the Univerisity requirements, Mechanical graduates are highly encouraged to apply in PG Aeronautics. However, just be a little careful as job in Aeronautics is not wide open, as far as I know. I am a grad of Aero. So I love Aero. But Aero is not that versatile, because its specific just for aircraft.
My recommendation would be do not go for PG in Aero.. keep up with Mechanical or systems.

This post is two years old, so I suspect that the OP has already decided whether to major in ME or Aero. However, I woud agree that ME is an excellent precursor to a graduate degree specializing in aero. As a mech e undergrad be sure to emphasize courses in fluid mechanics, solid mechanics (structures, plate theory etc), and dynamics (vibrations). Many mech e departments also offer at least one or two courses in introductory aeronautical engineeing at the undergrad level. Your ability to get into a good aero post grad program will depend more on your grades and GRE score than whether you majored in ME or Aero as an undergrad.

It actually Depends on the degree your Engineering, your marks, the Country your're applying in and the University.. If you're a Well Qualified Engineer nothing can Stop you man! Doesn't matter if you're an Aero. Engineer or Mech. Engineer "Talent" is a must!