Final answer:
The correct category for air taxis with Piston/Turboprop engines allowing up to 9 passengers, excluding turbojets, is category 703.
Step-by-step explanation:
The category you're referring to is for air taxis that utilize Piston/Turboprop engines and can carry up to 9 passengers, but does not include turbojets. The designation that matches this description is 703. This refers to a category of air transport operations that is defined by the capacity and type of aircraft, specifically excluding operations that use turbojet-powered aircraft.