Those rules u mention are for the route selection. Here the question is about route insertion. Longest Prefix does not play a role for inserting in the table, only for selecting a route.
Sinear is correct.
https://www.cisco.com/c/en/us/support/docs/ip/enhanced-interior-gateway-routing-protocol-eigrp/8651-21.html
"The longest prefix match always wins among the routes actually installed in the routing table, while the routing protocol with the lowest administrative distance always wins when installing routes into the routing table."
Ref: Route Selection in Cisco Routers – Cisco
“…
Building the Routing Table
…
As each routing process receives updates and other information, it chooses the best path to any given destination and attempts to install this path into the routing table. For instance, if EIGRP learns of a path toward 10.1.1.0/24, and decides this particular path is the best EIGRP path to this destination, it tries to install the path it has learned into the routing table.
The router decides whether or not to install the routes presented by the routing processes based on the administrative distance of the route in question. If this path has the lowest administrative distance to this destination (when compared to the other routes in the table), it's installed in the routing table. If this route isn't the route with the best administrative distance, then the route is rejected.
…”
A. route with the next hop that has the highest IP
Wrong answer.
B. route with the lowest cost
Wrong answer.
C. route with the lowest administrative distance
Correct answer.
D. route with the shortest prefix length
Wrong answer.
Installed and input are the same thing, don't overthink it. The reason the answer is C is because longest prefix isn't mentioned in one of the answers. So the next best thing to think of is the lowest admin distance
The answer is indeed C, but I'd like to correct an inaccuracy in your reasoning. The length of the prefix is the same for all of the routes, as is stated in the question. "R1 has learned route 10.10.10.0/24 via numerous routing protocols", meaning the prefix length is the same. Therefore, the next most relevant parameter is AD.
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