In any Apache Kafka cluster, there is always exactly one active Controller at any given time. This Controller is one of the brokers, elected through a consensus mechanism (like ZooKeeper or KRaft). Its primary responsibility is to manage the cluster's state, including partition leadership, broker failures, and topic creation/deletion. The number of brokers, topics, partitions, or consumers in the cluster does not alter this fundamental architectural principle of having a single active Controller to ensure consistent metadata management and avoid "split-brain" scenarios.

B. two: A Kafka cluster is designed with a single active controller to prevent conflicting state changes and ensure metadata consistency.

C. three: Having multiple active controllers is not supported by Kafka's architecture as it would lead to an inconsistent and unstable cluster state.

D. Four: While any of the four brokers is eligible to become the controller, only one broker is elected to be active in that role at any time.

1. Confluent Documentation, Apache Kafka® Internals: "One of the brokers in the cluster is designated as the controller. The controller is responsible for electing a leader for each partition." This statement confirms the single-controller design.

Source: Confluent Documentation, "Apache Kafka Internals" section.

2. Kreps, J., Narkhede, N., & Rao, J. (2011). Kafka: A Distributed Messaging System for Log Processing. In Proceedings of the NetDB '11: 6th International Workshop on Networking Meets Databases. "One of the brokers is elected as the 'controller'. This controller detects broker failures and is responsible for electing new leaders for all partitions on the failed broker."

Source: Section 3.2, "Distribution".

3. Narkhede, N., Shapira, G., & Palino, T. (2017). Kafka: The Definitive Guide. O'Reilly Media. "The controller is a broker that has additional responsibilities... At any given time, there is only one controller in a Kafka cluster."

Source: Chapter 6, "Data Delivery", section "Replication".