**Core Concept**
A cognizable offence refers to a crime that is serious enough for a police officer to make an arrest without a warrant, typically involving a breach of public peace, violence, or other severe infractions.

**Why the Correct Answer is Right**
In a cognizable offence, the police have the authority to arrest an individual without a warrant, as it is deemed a serious threat to public order or safety. This provision is enshrined in the Code of Criminal Procedure (CrPC) and allows law enforcement to take swift action in situations where they believe a person has committed a cognizable offence. The police officer's discretion in such cases is guided by the Indian Penal Code (IPC) and the CrPC, which specify the types of offences that are considered cognizable.

**Why Each Wrong Option is Incorrect**
**Option A:** An offence that can be forgiven is not a cognizable offence, as forgiveness is a concept related to the pardon of a crime rather than the police's authority to make an arrest.

**Option B:** An offence in which a person can be arrested but with a warrant is not a cognizable offence, as the police must obtain a warrant from a magistrate before making the arrest.

**Option D:** An offence in which bail cannot be granted is related to non-bailable offences, not cognizable offences. While some non-bailable offences are also cognizable, not all cognizable offences are non-bailable.

**Clinical Pearl / High-Yield Fact**
It is essential for medical professionals to understand the distinction between cognizable and non-cognizable offences, as this affects the police's authority to investigate and make arrests in cases related to medical professionals, such as alleged medical negligence or malpractice.

**✓ Correct Answer: C. Offence in which a person can be arrested even without a warrant**