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Statement a: collection of colleterial gland forms the egg case in Cockroach.
Statement b: The development of Cockroach is hemimetabolous.

A. Both the statements, a and b, are correct and b is the reason for a
B. Both the statements, a and b, are correct but b is not the reason for a
C. Statement a is correct but statement b is wrong
D. Statement b is correct but statement a is wrong

Answer
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Hint: Colleterial glands are the branched organs present in the female genital apparatus of Cockroaches that helps in the secretion of an ootheca over the fertilized eggs. Hemimetabolous development is the incomplete metamorphosis where insects grow to adult forms by gradual changes in their morphology.

Complete answer:
Cockroaches are Dioecious and they have the segmented body divisible in three parts i.e. Head, Thorax and Abdomen. Testes are located in 4-6 segments of the abdomen and each testes has several testicular lobules. Vas deferens conduct the sperms from testes to the seminal vesicle where they are turned into a mass called Spermatophore.
In females, the ovaries are located in the 2nd -6th abdominal segment and each ovary has filament like 8 ovarioles or ovarian tubules. The oviduct arises from each ovary and unites to form a common oviduct/vagina. A pair of Spermatheca is present in the 6th segment for storing sperms. A pair of branched Colleterial glands are also present.
Following copulation, the sperms are transferred and stored in the Spermatheca. Each ovariole produces an egg and hence 16 eggs are produced.
After fertilization, these eggs are arranged in 2 rows of 8 each and ootheca is secreted over them by the Colleterial glands. The female produces 9-10 ootheca each containing 14-16 eggs.
The female then delivers these ootheca to a safe place with relative humidity near a food source.
The young ones are developed and called Nymph, lacking wings. Only next to the last Nymphal stage have wing pads while only adults have wings. This development is called Paurometabolous development.

Hence, the correct answer is option (C).

Note: The collateral glands present in females produce secretions that cover two parallel rows of eggs during oviposition. There are two collateral glands present in the female cockroach. The female produces 9-10 ootheca each containing 14-16 eggs.