Explanation:

This complex scenario involves the principles of provocation and transferred malice under the Indian Penal Code (IPC). We need to analyze the elements of culpable homicide, murder, and their exceptions. **Analysis of Options:** * **Option (1) 'A' has not committed any offence as there was neither intention nor knowledge that he is likely to kill 'Z' who is near him but out of sight:** This option is incorrect. While 'A' did not intend to kill 'Z' specifically, and 'Z' was out of sight, the act of firing a pistol at 'Y' with the intention or knowledge of causing death or grievous injury to 'Y' is an unlawful act. The law of 'transferred malice' (Section 301 IPC) comes into play here. When an offender intends to cause the death of one person but, by mistake or accident, causes the death of another, the offense is treated as if the intended person's death had been caused. Therefore, 'A' cannot claim 'no offence' simply because the victim was unintended. An offense has certainly been committed. * **Option (2) 'A' has committed the offence of culpable homicide not amounting to murder:** This is the correct answer. Let's break down the reasoning: 1. **Grave and Sudden Provocation:** The scenario explicitly states that 'Y' gives 'grave and sudden provocation' to 'A'. Exception 1 to Section 300 of the IPC states that culpable homicide is not murder if the offender, whilst deprived of the power of self-control by grave and sudden provocation, causes the death of the person who gave the provocation, or causes the death of any other person by mistake or accident. If 'A' had killed 'Y' under this provocation, it would have been culpable homicide not amounting to murder. 2. **Transferred Malice (Section 301 IPC):** Section 301 of the IPC, known as the doctrine of transferred malice or transfer of motive, states: "If a person, by doing an act which he intends or knows to be likely to cause death, commits culpable homicide by causing the death of any person, whose death he neither intends nor knows to be likely to cause, the culpable homicide committed by the offender is of the description of which it would have been if he had caused the death of the person whose death he intended or knew to be likely to cause." In this case, 'A' intended to cause the death of 'Y' (or at least knew it was likely to cause death) but accidentally killed 'Z'. According to Section 301, the culpability for killing 'Z' will be the same as if 'A' had killed 'Y'. 3. **Combination:** Since killing 'Y' under grave and sudden provocation would have been culpable homicide not amounting to murder (due to Exception 1 to Section 300), by virtue of Section 301, killing 'Z' under the same circumstances also amounts to culpable homicide not amounting to murder. * **Option (3) 'A' has committed the offence of causing death by negligence:** Causing death by negligence (Section 304A IPC) applies when death is caused by a rash or negligent act *not amounting to culpable homicide*. Here, 'A' fired a pistol, an act that clearly demonstrates intention or knowledge of causing death or grievous bodily injury to 'Y'. This level of mens rea goes beyond mere negligence. Therefore, this option is incorrect. * **Option (4) 'A' has committed the offence of culpable homicide amounting to murder:** This option would be correct if the act of killing 'Y' (or 'Z' by transferred malice) did not fall under any of the exceptions to Section 300. However, the presence of 'grave and sudden provocation' is a specific exception that reduces the offense from murder to culpable homicide not amounting to murder. Therefore, this option is incorrect. In conclusion, the combination of grave and sudden provocation (Exception 1 to Section 300) and the doctrine of transferred malice (Section 301) leads to the conclusion that 'A' is guilty of culpable homicide not amounting to murder.