Final answer:
Roaches undergo gradual or incomplete metamorphosis, where the young stages resemble the adults and develop through successive molts, with the correct option being (c) gradual.
Step-by-step explanation:
The type of metamorphosis that roaches undergo is gradual metamorphosis, which is also known as incomplete metamorphosis.
This process involves the young resembling wingless adults and gradually developing larger wing buds during consecutive molts, eventually resulting in functional wings and sex organs in the last molt. Unlike complete metamorphosis, which includes distinct life cycle stages of egg, larva, pupa, and adult, in gradual metamorphosis, each stage looks more similar to the adult than in the complete metamorphosis process.
Therefore, the correct option is (c) gradual, and I have mentioned the correct option in the final answer.