We know that , in cockroach male and female are seprated and male is bigger than female . according to question anal style are thread like appendage . they are found in 9th segment of male cokroach and anal style are absence of female cokroach.

The correct answer to the question is option 'A' (anal styles in males).

Cockroaches are a diverse group of insects belonging to the order Blattodea. They are found in various habitats worldwide and are known for their ability to adapt to different environments. In order to distinguish between male and female cockroaches, external characteristics are often observed.

Anal styles or anal cerci are structures located at the posterior end of the cockroach's abdomen. These structures differ between males and females and can be used to distinguish them.

Explanation:
1. Anal styles in males: Anal styles are specialized structures found in male cockroaches. They are located on the 10th segment of the abdomen, just below the cerci. Anal styles are elongated and often curved or hook-shaped in appearance. They play a role in mating and are used by males to grasp and hold onto the female during copulation. The presence of anal styles is a reliable external characteristic that can be used to identify male cockroaches.

2. Anal cerci in females: Anal cerci are structures found in female cockroaches. They are also located on the 10th segment of the abdomen, just above the anal opening. The cerci in females are shorter and more rounded compared to the anal styles in males. While the anal cerci in females do not have a specific function in mating, they may play a role in sensing the environment and detecting potential threats.

3. Antennae: The presence or absence of antennae is not a reliable characteristic for distinguishing between male and female cockroaches. Both male and female cockroaches have antennae, which are important sensory organs used for detecting the environment, locating food, and communicating with other individuals.

In conclusion, male and female cockroaches can be distinguished externally through the presence of anal styles in males. The anal styles are specialized structures involved in mating and are located on the 10th segment of the male's abdomen. On the other hand, female cockroaches have anal cerci, which are shorter and more rounded compared to the anal styles. Antennae are present in both male and female cockroaches and are not reliable characteristics for distinguishing between the sexes.