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 192.168.1.254/24 and it needs to speak with the router, the router must have an interface on the 192.168.1.0/24 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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