When the Chief Justice of a High Court acts in an administrative capacity, he is subject to Option 1: the writ jurisdiction of any of the other judges of the High Court.

The Chief Justice of a High Court, while primarily responsible for the judicial functions of the court, also has administrative responsibilities. These administrative functions involve managing the court`s operations, including the allocation of cases, appointment of staff, and overall court administration. In the performance of these administrative duties, the Chief Justice is subject to certain checks and balances.

Option 1 states that the Chief Justice is subject to the writ jurisdiction of any of the other judges of the High Court. This means that if any other judge of the High Court finds that the administrative actions or decisions of the Chief Justice are arbitrary, illegal, or in violation of any fundamental rights, they can exercise their writ jurisdiction and issue appropriate directions or orders to rectify the situation.

The writ jurisdiction is a vital power vested in the High Court judges to ensure the rule of law and protect individuals` rights. It allows them to intervene when there is a violation of legal rights or when there is a need to correct administrative decisions that may be unlawful or unfair. This jurisdiction acts as a check on the Chief Justice`s administrative actions and ensures that they are in conformity with the principles of justice, fairness, and constitutional validity.

It is important to note that the Chief Justice of a High Court holds a position of significant authority, and therefore, subjecting their administrative actions to the writ jurisdiction of other judges helps maintain a system of checks and balances within the court. This arrangement ensures that the administrative decisions made by the Chief Justice are not beyond scrutiny and can be reviewed by their peers if necessary.

In contrast, Options 2, 3, and 4 are not directly applicable to the administrative functions of the Chief Justice of a High Court. Option 2 suggests that the Chief Justice of India exercises special control over the Chief Justice of a High Court in their administrative capacity. While the Chief Justice of India holds a position of authority at the national level, their control is primarily related to matters of policy, allocation of cases among different High Courts, and overall coordination of the judiciary. It does not specifically address the administrative actions of the Chief Justice of a High Court within their own court.

Options 3 and 4 pertain to the discretionary powers of the Governor of the state and special powers provided to the Chief Minister. However, these powers are generally not directly involved in the administrative functioning of the Chief Justice of a High Court. The Governor and Chief Minister are political authorities, and their powers primarily revolve around the executive and political aspects of governance, rather than the administration of the court.

Therefore, considering the options provided, Option 1: the writ jurisdiction of any of the other judges of the High Court, is the most relevant and appropriate choice as it aligns with the principles of judicial review and the need for checks and balances in the administration of justice.