Which pair of an Ethernet cable does a router transmit on?
According to this diagram from the Wikipedia page on crossovers, a network card (NIC) will transmit on 1 and 2, so a hub/router/switch will transmit on 3 and 6.



The ethernet twisted pair page states:


  A 10BASE-T or 100BASE-TX node such as a 
  PC, with a connector called medium dependent interfaces (MDI),
  transmits on pin 1 and 2 and receives on pin 3 and 6 to a network
  device using a "straight-through" cable.


It hasn't actually mattered in a long time though - auto-MDIX has been around for a decade or so.