Why a router does not have only one IP address (i.e. for itself). and why a unique IP address need to be associated with each interface? Whats the scenario which neccessiates each interface to have an IP addresses?(TCP IP)

The router requires a unique IP address for each interface so that the hosts on each segment can communicate with the router's interface. If a computer's IP is and it needs to speak with the router, the router must have an interface on the subnet. The computer will not be able to directly communicate with another one of the router's IP addresses that may be servicing a different subnet.

This article may help you understand how lan routing works: http://www.itgeared.com/articles/1054-how-ip-packets-are-routed-on-local-area/

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