737NG...land with F15....then go with F15...the flaps run too slowly!
All the touch and goes I have ever done/seen have been with flap 30/40 and flap 15 selected after touchdown - ok if the runway is long enough!
What is the purpose of these particular touch and goes?
Apart from giving (new) pilots practice at take off and landings on the real machine after the simulator (which in turn is a requirement for type rating etc), one purpose is to save time! If you landed and then taxied back to the take off point it would take a lot longer and also you can cool the brakes down a bit by leaving the gear down every so often in the circuit!