Design Entrance Exam

Do, absolutely, go for it. It is much better than going for an MBA (unless the MBA serves a grand plan of yours). With an M.Des in hand, sooner or later you'll find yourself wanted badly by the industry. The Indian manufacturing/services mindset is changing, and we are moving towards more of a 'build a brand' mindset. The things that'd get us there are:
a) Greatly designed products and services
b) Great marketing
A design course would not just give you the skills that the industry needs, but also a way of thinking that unlocks doors.
I personally have not gone for a Master's degree after Bachelors in engineering, but being in touch with designers has made me hold them in high respect.
For entrepreneurs:
Design thinking makes you see opportunities, and that's great for an entrepreneurial mind.
For professionals:
The pay may be low (though that's changing too), but some of the projects you might be on will have a potentially great impact.
That said, it's really hard work being a designer if you're up for it and for a prolonged period of struggle, a world of wonder awaits you.