A pilot shall not operate as pilot-in-command of an aeroplane carrying passengers unless the pilot has?

For a pilot to operate as pilot-in-command of an aeroplane carrying passengers, they must adhere to specific recency requirements to ensure safety and proficiency. According to aviation regulations, a pilot is required to have accomplished at least three take-offs and three landings as the pilot flying within the preceding 90 days to carry passengers safely. This requirement is in place because take-offs and landings are critical phases of flight that involve particular skills and decision-making.

The emphasis on the landings being performed as the pilot flying corresponds directly with maintaining practical flying skills, ensuring the pilot is well-prepared to handle the aircraft in everyday operational scenarios, especially when passengers are aboard. This recency rule helps ensure that pilots maintain their proficiency and are familiar with the aircraft's handling characteristics.

The other options either specify the wrong timeframe or do not adequately reflect the necessary operational requirements for carrying passengers. For instance, options that mention shorter timeframes do not align with the regulatory standards designed to guarantee pilot competence and safety when passengers are involved.