Explanation:

- Option 1: Habeas corpus

- This writ is used to protect personal liberty. It commands a person who has detained another to produce the body of the person in court. Not used to command a public authority to perform its duty.

- Option 2: Qua warranto

- This writ challenges a person’s right to hold a public office. It’s used when someone is unlawfully occupying a post.

- Option 3: Mandamus

- Mandamus means “we command”. It is used to command a public authority to perform its public duty, which it has failed or refused to do.

- This is the correct answer.

- Option 4: Prohibition

- This writ is issued by a higher court to stop a lower court or tribunal from exceeding its jurisdiction.

The correct answer is Option 3: Mandamus.