Step 1: Understanding the Concept:
The question provides a definition and asks to identify the corresponding type of contract from the Indian Contract Act, 1872.
Step 2: Detailed Explanation:
The definition provided is: "A contract to perform the promise, or discharge the liability, of a third person in case of his default".
This is the precise legal definition of a "Contract of Guarantee" as given in Section 126 of the Indian Contract Act.
The section identifies three parties in such a contract:
1. Surety: The person who gives the guarantee.
2. Principal Debtor: The person in respect of whose default the guarantee is given.
3. Creditor: The person to whom the guarantee is given.
The definition in the question perfectly matches this legal concept. It is not a contract of indemnity, which involves a promise to save someone from loss, nor is it a partnership. "Default" is an event, not a type of contract.
Step 3: Final Answer:
The question directly quotes the definition of a contract of guarantee. Therefore, option (A) is the correct answer.