Explanation:

First is correct.
Certiorari –
• It means ‘to be certified’ or ‘to be informed’.
• It is issued by a higher court to a lower court or tribunal either to transfer a case pending with the latter to it or to squash the order-of the latter in a case.
• It is issued on the grounds of excess of jurisdiction or lack of jurisdiction or error of law.
• Prohibition is only preventive, but certiorari is both preventive as well as curative.
• Till recently, the writ of certiorari could be issued only against judicial and quasi-judicial authorities.
• In 1991, the Supreme Court ruled that the certiorari can be issued even against administrative authorities affecting rights of individuals.
• Like prohibition, certiorari is also not available against legislative bodies and private individuals or bodies.

Second statement is incorrect.
Prohibition –
• It means ‘to forbid’.
• It is issued by a higher court to a lower court or tribunal to prevent the latter from exceeding its jurisdiction or usurping a jurisdiction.
• Mandamus directs activity, but prohibition directs inactivity.
• The writ of prohibition can be issued only against judicial and quasi-judicial authorities.
• It is not available against administrative authorities, legislative bodies, and private individuals or bodies.

Third is correct.
Quo-Warranto –
• It means ‘by what authority or warrant’.
• It is issued by the court to enquire into the legality of claim of a person to a public office.
• It prevents illegal usurpation of public office by a person.
• The writ can be issued only in case of a substantive public office of a permanent character created by a statute or by the Constitution.
• It cannot be issued in cases of ministerial office or private office.
• Unlike the other four writs, this can be sought by any interested person and not necessarily by the aggrieved person.

Fourth is incorrect.
Mandamus –
• It means ‘we command’.
• It is a command issued by the court to a public official asking him to perform his official duties that he has failed or refused to perform.
• It can also be issued against any public body, a corporation, an inferior court, a tribunal or government for the same purpose.
The writ of mandamus cannot be issued -

1. against a private individual or body;
2. to enforce departmental instruction that does not possess statutory force;
3. when the duty is discretionary and not mandatory;
4. to enforce a contractual obligation;
5. against the president of India or the state governors; and
6. against the chief justice of a high court acting in judicial capacity.