Which of the following is a valid reason for a member to petition for winding up?

Petitioning for winding up a business entity is a serious decision that can arise from various circumstances, particularly in cases of internal conflict or dysfunction within the management structure. A deadlock in management signifies a situation where the members or shareholders are unable to reach an agreement on critical business decisions, leading to paralysis in the operation of the business. This type of deadlock can significantly hinder the company's ability to function effectively, preventing it from making necessary strategic decisions or pursuing growth opportunities.

In such scenarios, a member may seek judicial intervention to resolve the deadlock or to facilitate the process of winding up the business altogether, especially if continuing operations is not feasible. This legal remedy is particularly relevant when the conflict is profound enough to threaten the viability of the business or when the parties involved cannot reconcile their differences.

The other options, such as profit increase, market expansion, and increase in share value, do not provide substantial grounds for petitioning to wind up a business. These are typically indicators of a thriving business environment and would not lead members to petition for dissolution, as they imply that the business is operating successfully and with growth potential rather than facing internal turmoil.