Hi Singh
A transponder emits information from the aircraft which will appear on a radar display. This information may be displayed as a series of numbers or more likely as (after automatic decoding)the aircraft callsign ,it's level("height") and its destinaton and speed. In certain airspace there is "MODE S"(but thats for another time.)which supplies even more information. In the event it fails (on the radar I use)I would see a "primary" blip ie a raw unprocessed blob. This is likely to be fairly similar throughout the world where the two systems are in use. In the event that the airspace radar is secondary(ie relying on transponder derived information only) ...then the blip will dissappear completely. One of my area colleagues will be along in a moment to explain what happens in that case.
I can't comment on Indian ATC
In my experience transponder failure does happen but in many cases the aircraft is equipped with more than one.
Regards