Which of the following activities can be performed under the privileges of inspection authorization?

The correct answer is the activity that involves approving the return-to-service of a major repair in accordance with an Airworthiness Directive (AD). Under the privileges of an inspection authorization, an individual can perform inspections and approve repairs to ensure that aircraft and their components meet the regulatory requirements for safety and airworthiness.

When a major repair is conducted, it must adhere to the guidelines outlined in the applicable ADs. This process ensures that all necessary corrective actions have been taken to address safety concerns and maintain the operational integrity of the aircraft. By approving the return-to-service in compliance with an AD, the IA confirms that the repair meets the standards set forth by the FAA and is essential for maintaining the airworthiness of the aircraft.

Conversely, while overhaul and approval of a float type carburetor could also be within the scope of an IA's privileges, it’s not a broad enough activity compared to the specific compliance with ADs. The exchange of engines of different makes involves complex regulatory considerations that may involve airworthiness issues, while annual inspections, although a vital function, are just one type of inspection activity and do not capture the broader capabilities provided under the IA. Hence, the option related to AD compliance is the one that exemplifies the responsibilities and authority vested in