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The command that provides detailed information including input and output rates for interfaces is "show interfaces." This command displays a comprehensive overview of all interfaces on a router or switch, including their status, protocol state, and various performance metrics such as input/output rates, error counts, and more.

When you use "show interfaces," you get detailed statistics that can help network engineers troubleshoot performance issues, assess interface utilization, and understand how much traffic is passing through each interface. This includes valuable information such as the number of packets and bytes sent and received, which is crucial for monitoring network performance and capacity planning.

Other commands listed serve different purposes. For instance, "show ip route" presents the routing table and summarizes how the router reaches various networks but does not provide interface-specific metrics. "Show ip interface brief" offers a summarized view of interface statuses and IP addressing but lacks the detailed input/output statistics that "show interfaces" provides. Lastly, "show service-module" generally pertains to service modules and their statistics, which is not focused on interface traffic rates. Thus, "show interfaces" is the correct command for retrieving detailed input and output rates.