Metamorphosis is the process of development of organisms after hatching or birth. Insects that go through three stages of change in their life cycle have an incomplete metamorphosis. The first stage is the egg. During this time, the insect will hatch into a form, called a nymph. The nymph is basically a small version of the adult insect. Once a nymph outgrows its exoskeleton it will go through a process called moulting which is to leave the old skin or exoskeleton behind. The new skin will harden and become the new exoskeleton. This will happen many times until the insect finally becomes an adult. So, the correct answer is option B.

The mushroom gland is a large accessory male reproductive gland in the cockroach, which is whitish in colour and situated at the junction of vasa deferentia with the ejaculatory duct. It has a mass of glandular tubules of three kinds, the peripheral long tubules or utriculi majors, the central tubules are small short tubules or utriculi breviores and behind the short central tubules are some short but more bulbous tubules forming the seminal vesicles filled with sperms. 

Genital or brood pouch is a large boat-shaped structure whose floor is formed by the 7th sternite, roof and sides are formed by the 8th and 9th sternites. The genital pouch can be divided into a genital chamber into which vagina opens and an oothecal chamber where oothecae are formed. The genital chamber also receives the accessory reproductive glands. 

The genital pouch of female cockroach can be divided into two parts. The anterior smaller part containing the openings of female gonopore, pores of spermathecae and collateral glands is called genital chamber, while the larger posterior part in which ootheca is formed is called oothecal chamber or vestibulum. Oviduct doesn't open into the genital chamber.

Cockroach and earthworm have common type of  spermatheca The spermathecae receive and store  sperm cells during copulation .

Each ovary is formed of a group of eight ovarian tubules or ovarioles containing a chain of developing ova. An ovariole is made up of an epithelial layer resting on a basement membrane and enclosed externally in a connective tissue coat. Hence In cockroach, an ovary is formed of 8 ovarioles.

The gizzard is an outer layer of thick circular muscles and has a thick cuticle forming six highly chitinous plate called teeth. Gizzard helps in grinding the food particles. The entire foregut is lined by the cuticle. Gastric caecae are present in the foregut and midgut., which secrete digestive juice. A stomadaeal valve is present in between the gizzard and the midgut (mesenteron).

Cockroach follow a hemimetabolous mode of metamorphosis. It is also known as gradual metamorphosis. The hemimetabolous life cycle consists of egg, nymph and adult.

In cockroach, the fertilized eggs are encased in a casing called the oothecae. Ootheca of cockroach contains 16 fertilized eggs in two rows (8 + 8). 

In Cockroach, there are a pair of collaterial glands. A pair of branched collaterial glands open into genital chamber. The secretion of collaterial glands secrete oothecal case.

The phallic or conglobate gland is an elongated and flattened gland that lies below ejaculatory duct in males. The posterior end is narrow and opens separately by the side of the male genital pore.

The female reproductive system has two large ovaries that are present laterally in the 2nd to the 6th abdominal segments. A group of eight ovarian tubules forms one ovary. They contain a chain of developing ova. The fertilized eggs are encased in a casing called the oothecae. Female cockroaches produce around 9 to 10 oothecae which contain around 14 to 16 eggs each.

The nymphal stage begins when the egg hatches and ends with the emergence of the adult. The number of times a Periplaneta americana moults 13 times. The first instar American cockroach is white immediately after hatching then becomes a greyish brown.

A mushroom-shaped gland is present in the 6th and 7th abdominal segments of a male cockroach. It acts as an accessory reproductive gland. The mushroom gland has two types of tubules. These tubules open into the ejaculatory duct or ductus ejaculatorius in the 7th segment.

A mushroom gland is a large and whitish accessory gland located at the junction of vasa deferential and ejaculatory duct. It is formed of three types of small sac-like tubules 

The colleterial glands of insects are organs associated with the female genital apparatus. In cockroaches, these glands produce secretions that cover two parallel rows of eggs during oviposition, and in oviparous species, these secretions become the tanned, sculpted, rigid outer casing of the ootheca.

A mushroom-shaped gland is present in 6th and 7th abdominal segments of a male cockroach. It acts as an accessory reproductive gland. The mushroom gland has two types of tubules:

1. Testes lie dorsolaterally in the 4th and 5th abdominal segments, and they are the region of sperm production.
   2. Vas deferens are a pair of ducts arising from the testis as very thin whitish tubes, they continue posterioventrally beneath the rectum. They unite at a short distance into the ejaculatory duct.
   3. Mushroom gland is a large accessory reproductive gland, whitish in colour and situated at the junction of vasa deferentia with the ejaculatory duct. It has a mass of glandular tubules of two kinds; utriculi majores and utriculi breviores.
   4. The sperms produced from testes, while the cockroach is still young, are brought by the vasa deferentia into the seminal vesicles for storage. The sperms in the seminal vesicles are glued together in the form of bundles called spermatophores. 
   So, the correct option is 'Seminal vesicles'.

In male cockroach, from the sides of the 9th sternum, there arises a paired, small unjointed outgrowths called anal styles. These structures are sensitive to touch.These are absent in female cockroach. Nervous system is located ventrally. There are 100-150 Malpighian tubules. Grinding of food is carried our by mouth parts and gizzard.

1. The body of female cockroach is relatively larger than the male.

2. The abdomen of female cockroach is boat-shaped and the last segment is blunt.

3. The wings of female cockroach are smaller than that of the males and extend up to the tip of the abdomen.

4. The antennae are relatively larger than that of the males.

5. Only a pair of anal cerci is present in of female cockroach.

6. The sternum of mesothorax is bifid.

So the correct option is 'anal styles'.

All cockroaches develop by completing a life cycle consisting of three distinct stages: egg, nymph, and adult.

(A) Phallomere - The external genitalia

Sexual dimorphism is the differences in appearance between males and females of the same species. The adult males have full wings covering their body, while females have only tiny wing stubs, their tegmina (forewings) being around a fourth of their body length.
Therefore, the correct answer is option D.

Sex pheromones are released by an organism to attract an individual for mating. Cockroaches form the dominance hierarchies based on pheromone badges, while females use the same pheromone for male choice.
Therefore, the correct answer is option B.

The intersegmental membrane between the 5th and 6th terga is depressed on either side of the stink gland. These glands are present in both male and female cockroaches and produce a secretion with a characteristic odour. The secretion is a pheromone which helps to attract the opposite sex.
Therefore, the correct answer is option C.

Eggs of cockroach are centrolecithal. During cytokinesis, centrolecithal zygotes undergo meroblastic cleavage, where the cleavage plane extends only to the accumulated yolk and is superficial. This is due to the large dense yolk found within centrolecithal eggs and helps in delayed embryonic development.

The colleterial glands open into the vestibulum and secrete most of the protein and tanning agent. The protein may not be directly concerned with ootheca formation, while the latter probably secretes the alkali-resistant outer layer of the ootheca.
The anterior and posterior parts of cockroach secreting the structural protein which produces most of the material used in the formation of the ootheca.

Cockroach eggs hatch because of the combined pressure of the hatchlings within. Upon emerging from the egg case, or ootheca, this immature form of cockroach is known as a nymph or baby cockroach. Nymphs are bright white in color initially. Cockroach nymphs are grayish-brown in color and darken with each progressive molt.  Cockroach nymphs undergo a series of molts. They emerge as full adults from their final molt.

The abdomen is made up of 10 segments. The 7th, 8th and 9th sterna form a genital pouch in females. In males, the genital pouch is present at the hind end of the abdomen. The male cockroach has thread-like anal styles, which are missing in the female cockroach. Hence, Male Cockroach is identified by the presence of anal style.

In cockroaches, the sperm is stored in the seminal vesicles and are glued together in the form of bundles called spermatophores and discharged during copulation. Seminal vesicles are the part of the ejaculatory duct.

Collaterial glands are present in female cockroach as part of reproductive system. These glands are branched tubular glands opening independently on the dorsal side of the genital chamber. The secretion produced by these glands forms the oothecal case of ootheca.

In female cockroach, each ovary is formed of a group of eight ovarian tubules or ovarioles, containing a chain of developing ova.

The development of Periplaneta americana is paurometabolous, i.e., there is development through nymphal stage.