Step 1: Understanding the Concept:
The question asks for the definition of a 'cognizable offence' as provided in the Cr.P.C. This is a key definition that determines the extent of police powers at the initial stage of an investigation.
Step 2: Detailed Explanation:
Section 2(c) of the Cr.P.C. defines a "cognizable offence" as an offence for which, and "cognizable case" means a case in which, a police officer may, in accordance with the First Schedule or under any other law for the time being in force, arrest without a warrant.
These are generally more serious offences (e.g., murder, robbery, kidnapping). The law empowers the police to act swiftly in such cases by arresting the suspect without needing to first obtain a warrant from a court.
- Option (B) describes a non-cognizable offence, defined in Section 2(l).
- Option (C) is also incorrect as the defining feature is the ability to arrest \textit{without} permission.
- Option (D) relates to the limited powers of arrest by a private person under Section 43, which is a different concept.
Step 3: Final Answer:
The definition in Section 2(c) explicitly states that in a cognizable offence, a police officer may arrest without a warrant. Therefore, option (A) is the correct answer.