Under which condition will the ATTCS engage?

The correct condition for the engagement of the Automatic Takeoff Thrust Control System (ATTCS) is when the thrust levers are in TOGA (Takeoff/Go-Around) and the N1 split exceeds 15%. This condition ensures that the system can provide maximum thrust to the operating engine if one engine experiences a failure during takeoff.

When thrust levers are set to the TOGA position, the system is primed to provide the necessary thrust for takeoff, while the requirement for the N1 split to be greater than 15% signifies that there is a significant difference in thrust between the engines, which indicates a possible asymmetrical thrust situation. This activation is critical in maintaining safe operation and performance during takeoff under abnormal conditions.

The other options presented are relevant to the aircraft's operating conditions but do not directly relate to the conditions necessary for the engagement of the ATTCS. For instance, while specific flap settings, landing gear position, or altitude may have significance in broader operational contexts, they do not dictate the activation of the ATTCS. Therefore, the specific combination of thrust lever position and N1 split is what triggers the system's engagement, ensuring that pilots have the necessary thrust management support during critical phases of flight.