What type of MC Cable is permitted to be installed underground under a building without a raceway?

The correct type of MC (Metal-clad) cable that is permitted to be installed underground under a building without a raceway is direct burial MC cable. This type of cable is specifically designed to withstand the conditions associated with being buried, including moisture and potential physical stress. Direct burial MC cable has robust insulation and sheathing that provides protection against water ingress and is suitable for use in environments that could expose the wiring to damp or wet conditions.

In contrast, options mentioning damp and wet locations or rough service do not directly relate to underground installations without the use of a raceway. While MC cables that are rated for damp and wet locations may be used in specific situations, they still typically require a raceway when installed underground. Rough service refers to a resilience to physical abrasion or impact but is not specific to underground usage or alternatives to raceway installations. Therefore, direct burial MC cable is the appropriate choice for this specific application.