To solve this question, we need to critically analyze each of the given characteristics with respect to the anatomy of a cockroach and identify the incorrect one.
Option A: "A ring of gastric caeca is present at the junction of midgut and hind gut."
This statement is incorrect. In cockroaches, a ring of gastric caeca is present at the junction of the foregut and midgut. Thus, the gastric caeca serve to increase the surface area for digestion and play a role in the initial digestion of food. They are not located at the junction of the midgut and hindgut, making this option the correct answer to the question posed.
Option B: "Hypopharynx lies within the cavity enclosed by the mouth parts."
This statement is correct. The hypopharynx is a part of the mouthparts of a cockroach, located between the maxillae, and acts like a tongue, involved in manipulating food.
Option C: "In females, $7^{th}-9^{th}$ sterna together form a genital pouch."
This statement is accurate. In female cockroaches, the 7th to 9th abdominal segments are modified to form a brood chamber, also known as a genital pouch, which serves to carry the developing eggs.
Option D: "$10^{th}$ abdominal segment in both sexes, bears a pair of anal cerci."
This statement is correct. Both male and female cockroaches indeed have a pair of anal cerci on the 10th abdominal segment, which are sensory organs used to detect movement in the environment.
Given the explanations and elimination process, the statement in Option A is identified as incorrect since it provides a factually inaccurate description of the digestive anatomy of cockroaches.
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is : 
AB is a part of an electrical circuit (see figure). The potential difference \(V_A - V_B\), at the instant when current \(i = 2\) A and is increasing at a rate of 1 amp/second is:
In certain areas of the world, cockroaches are also known as waterbugs. These are one of the oldest insects whose fossils are 320 million years old. They are commonly known for ‘leaving behind stinky smells’, attacking household food items, and are considered carriers of diseases and hence are despised everywhere they are found.
Their average length is 4 cm and they are mainly reddish-brown in color. These insects have yellowish margins on the pronotum. The body of the cockroach is distinctly segmented, dorso-ventrally flattened, and covered by a shining brown exoskeleton.
The body can be divided into three different parts such as the head, thorax, and abdomen. Wings that are darker than the body itself usually cover the dorsal body surface. By nature, cockroaches are nocturnal and omnivorous animals.

Read More: Cockroach Life Cycle