I bought AC 2 days back... 1st day it was fine... but suddenly it stops working on 2nd day... In my area there is lots problem of electricity fluctuation... so I just want to know that...

Fluctuating power can burn out the compressor.

Where are you located and what voltage? A brownout, low voltage, will burn out the compressor.

What exactly stopped working and what kind of AC are you talking about? Did everything stop working? Is this a window unit? Low voltage will burn out the fan and compressor, but it depends on the voltage. A slight drop in voltage that is not below the minimum voltage will do no harm, but if you have a 240 volt unit and have less than 190 volts it can burn it up unless the safeties kick it off from overheating in time.