Aircraft carriers are so huge and slow moving, with submarines these can be neutralized within minutes, rendering the aircraft carrier only an expensive (including the human resource and aircrafts) coffins. To refresh your memory, MIGs were used to kick the hell out of the infiltrators during Kargil event. At your so called hypothetical situations, there is no scope of an aircraft carrier. The airfields are so close that within minutes a couple of squadrons can kick our enemy's backs. Aircraft carrier by the time can get nearer to a range where fighters can fly off, the fighters from airfields from border would have made couple of strikes. Again, aircraft carrier was not used during Kargil event and aircrafts within the border area were kicked into action.
Let it keep coming Rajeev, nice discussing with you. ;-)
