Hint: Moulting is the process of shedding old hair, feather or skin so as to regenerate new growth. It is very common in invertebrates.
To answer this question, we must know how the moulting is carried out in cockroaches. In cockroaches, it routinely casts off the outer covering or the exoskeleton of the body at specific times in its life cycle. When it is at an immature stage but has attained sufficient growth, it requires a large exoskeleton. For getting the larger exoskeleton, the old exoskeleton has to shed off or moult. The sensory cells from the body activate the neurosecretory cells in the brain. These cells secrete hormones which activates the corpora cardiaca to release prothoracicotropic hormone into the circulatory system. This PTTH stimulates the prothoracic gland to secrete a moulting hormone called Ecdysone. The prothoracic gland is present in the thorax. Moulting hormone then acts on the epidermis and stimulates cuticle formation.Whereas, Corpora allata secretes hormones which stimulate the process of metamorphosis. Metamorphosis is the series of changes which an insect undergoes to change from larvae to adult.
Additional information: Moulting is very common. Cats moult their fur around spring-summer time. Birds shed their feathers when not laying eggs. Snakes and lizards regularly shed their old skin. Amphibians often shed their skin and eat it.
Thus, the correct answer is (A). The moulting in cockroaches is induced by Prothoracic glands.
Note: Xylem is the complex tissue in plants whose function is to transport water and nutrients from roots to all parts of the plants. Xylem parenchyma is the only living component of the xylem tissue which stores starch and fat.