I have a 2950 switch, one PC is connected to one port of the switch with a IP address 10.0.0.1 and another PC is connected to one more port with a IP address 192.168.1.1
Both the PCs do not have a Gateway address and there is now router in the topology.
My question is will i be able to ping one PC from the other one. If yes how it will work?
Your post is not clear whether both PCs are in the same VLAN on the 2950. If they are not in the same VLAN then they will not be able to ping each other since there is no router to provide inter VLAN routing. If they are in the same VLAN then they are in the same broadcast domain and are able to talk to each other at layer 2. If the PCs will ARP for each other they will learn the MAC of each other and be able to ping.