Syncytial epidermis is found in

The correct option is Ascaris.

To understand why this is correct, let us break down the concepts of a syncytium and the epidermal structure of the given organisms step-by-step:

1. What is a Syncytial Epidermis?
An epidermis is described as syncytial (or coenocytic) when it consists of a continuous layer of cytoplasm containing multiple nuclei that are not separated by individual cell membranes. Instead of being divided into distinct cells, the cytoplasm is shared, forming a multinucleated state.

2. Analyzing the Organisms:
• Ascaris (Roundworm): Ascaris belongs to the phylum Nematoda. The body wall of Nematodes is covered by a tough, non-cellular cuticle secreted by the underlying epidermis. In Ascaris, this epidermis (also called hypodermis) is a syncytium containing many nuclei but no dividing cell walls. It projects inwards to form four longitudinal epidermal cords.
• Metaphire (Earthworm): Belonging to the phylum Annelida, its epidermis consists of a single layer of distinct columnar epithelial cells (including glandular cells, sensory cells, and supporting cells) rather than a syncytium.
• House fly and Periplaneta (Cockroach): These are arthropods. Their epidermis (hypodermis) is typically composed of a single layer of distinct, individual epithelial cells.

Therefore, a syncytial epidermis is a characteristic feature of the roundworm Ascaris.