The pneumotaxic centre and respiratory rhythm centres are two important components of the respiratory control system located in the brain. They play crucial roles in regulating the breathing process.

The correct answer is option 'A', which states that the pneumotaxic centre is present in the pons and the respiratory rhythm centres are present in the medulla oblongata. Let's discuss these centers in detail:

1. Pneumotaxic Centre:
- The pneumotaxic centre is located in the pons, which is a part of the brainstem.
- It is responsible for fine-tuning and controlling the rate and pattern of breathing.
- The main role of the pneumotaxic centre is to limit the duration of inspiration, preventing overinflation of the lungs.
- It does this by sending inhibitory signals to the inspiratory center in the medulla oblongata.

2. Respiratory Rhythm Centres:
- The respiratory rhythm centers are located in the medulla oblongata, which is also a part of the brainstem.
- There are two main respiratory rhythm centers: the dorsal respiratory group (DRG) and the ventral respiratory group (VRG).
- The DRG is responsible for generating the basic rhythm of breathing. It contains inspiratory neurons that initiate the process of inhalation.
- The VRG is involved in both inspiration and expiration. It contains both inspiratory and expiratory neurons.
- Together, these rhythm centers coordinate the contraction and relaxation of the respiratory muscles, ensuring regular and rhythmic breathing.

The role of the pneumotaxic center and the respiratory rhythm centers is interconnected. The respiratory rhythm centers generate the basic rhythm of breathing, while the pneumotaxic center fine-tunes this rhythm by regulating the duration and frequency of inspiration. This coordination between the two centers ensures efficient gas exchange and maintains a balance between oxygen and carbon dioxide levels in the body.

In conclusion, the pneumotaxic center is present in the pons, and the respiratory rhythm centers are located in the medulla oblongata. These centers work together to regulate the breathing process and maintain respiratory homeostasis.