Which rule governs the circumstances in which the court may strike out pleadings?

The correct choice highlights Rule 14.28, which specifically addresses the circumstances under which a court may strike out pleadings. This rule is crucial in civil proceedings as it sets out the legislative framework for ensuring that pleadings are relevant, clear, and properly formulated. Rule 14.28 allows the court to intervene when pleadings fail to meet the necessary legal standards, such as being scandalous, frivolous, vexatious, or lacking in any reasonable cause of action.

By having this specific rule in place, the court can maintain the integrity of the judicial process and prevent parties from engaging in litigation based on poorly drafted or irrelevant claims. This helps to streamline court proceedings by reducing the number of cases proceeding to trial that are unlikely to succeed due to their foundational issues.

The other choices correspond to different rules which do not specifically pertain to the striking out of pleadings, thus confirming that Rule 14.28 is the appropriate one that delineates the court's power in this aspect of civil practice and procedure in New South Wales.