Concept:
An ootheca is a protective capsule enclosing the eggs of a cockroach. It protects developing embryos from mechanical injury and environmental stress.
Step 1: Understand formation of ootheca.
After fertilization, the eggs are enclosed in a hard, brown, capsule-like structure called ootheca.
The covering material is secreted by specialized accessory reproductive glands.
Step 2: Identify the responsible gland.
In female cockroach, the colleterial glands secrete proteins and other substances that harden to form the oothecal wall.
Thus these glands directly participate in ootheca formation.
Step 3: Eliminate other options.
• Conglobate gland is associated with male reproductive system.
• Mushroom-shaped gland functions in male reproduction.
• Phallic gland is not responsible for ootheca formation.
Step 4: Final conclusion.
The ootheca is secreted by:
\[
\boxed{\text{Colleterial glands}}
\]
Hence option (C) is correct.