Step 1: Understanding the Question:
The question asks us to identify the specific writ that is issued to command a public authority or official to perform a mandatory public duty that they have failed or refused to perform.
We need to analyze the meaning and application of each writ listed in the options.
Step 2: Detailed Explanation:
• Mandamus is a Latin term which literally translates to "we command."
• The Writ of Mandamus is issued by a higher court to a lower court, tribunal, public official, or government body, directing them to perform a statutory or public duty that they are legally bound to do but have failed to execute.
• It can be filed by any person whose rights have been infringed due to the non-performance of a mandatory duty by a public authority.
• Habeas Corpus literally means "to have the body," and is issued to secure the release of a person who has been unlawfully detained, making Option (A) incorrect.
• Certiorari is issued by a higher court to quash the order of a lower court or quasi-judicial authority that has acted without or in excess of its jurisdiction, making Option (C) incorrect.
• Quo Warranto means "by what authority," and is issued to inquire into the legality of a person's claim to a public office, preventing usurpation of public offices, making Option (D) incorrect.
• Therefore, Mandamus is the writ used to command a public authority to perform its duty.
Step 3: Final Answer:
The writ issued to command a public authority to perform its duty is Mandamus, which corresponds to Option (B).