The correct answer is C) Sea chests, tail shaft wear down readings and rudder assembly. During a vessel dry-docking survey, the Class (the organization that certifies the vessel's compliance with safety and technical standards) typically requires the inspection of several key components. These include the sea chests (openings in the hull that allow water to enter the vessel's systems), the tail shaft wear down readings (to ensure the propeller shaft is not excessively worn), and the rudder assembly (to verify its proper functioning and structural integrity). This comprehensive inspection ensures the vessel's seaworthiness and compliance with the applicable regulations. The other options are incorrect because they do not cover the full scope of the typical Class-required inspections during a dry-docking survey. Option A focuses only on sea chests and tail shaft wear down, while Option B and D omit key components like the sea chests or the tail shaft wear down readings.