Which is a category and class of aircraft with respect to pilot certification?

The correct answer, "Airplane; single-engine land," accurately represents the category and class of aircraft in the context of pilot certification. The category refers to the broad classification of the aircraft—such as airplane, rotorcraft, glider, or lighter-than-air—while the class is a more specific designation within that category.

In this case, "airplane" is the category, and "single-engine land" is the class, indicating that the pilot is certified to operate an aircraft that is an airplane, has a single engine, and is intended for flight on land. This classification system is crucial for distinguishing the types of training and certification required for different aircraft and ensuring that pilots are qualified for the specific type of aircraft they intend to fly.

The other options do not represent both a category and a class correctly in the context of pilot certifications. While helicopters and balloons are legitimate categories, the classes they are presented with in those options do not align with standard pilot certification categories or classes as defined by aviation regulations. Therefore, the association of "airplane" with "single-engine land" is the only option that fulfills the requirement under pilot certification.