Explanation:

- Option 1: a judicial function

- Taking cognizance generally refers to the formal recognition by a court that a matter requires judicial review or action.

- It often involves the court's decision to proceed with a case.

- Correct Answer

- Option 2: an administrative function

- An administrative function usually involves tasks related to the management and execution of policies and regulations, not directly linked to judicial proceedings.

- Option 3: a supervisory function

- A supervisory function involves oversight and management duties, not typically associated with the judicial process of taking cognizance.

- Option 4: both (a) and (b)

- This option suggests that taking cognizance might be both judicial and administrative, which is not typically the case, as it primarily remains a judicial function.