Which of the following is an example of a nuisance alarm?

A nuisance alarm refers to an alarm that is triggered without the presence of a real emergency, often due to non-threatening conditions or system failures. In this context, the mechanical failure of a smoke detector fits the definition, as it may result in an alarm being activated when there is no actual fire or smoke present.

When a smoke detector malfunctions, it can lead to false alarms, causing unnecessary interruptions and potentially desensitizing occupants to genuine emergencies. This situation exemplifies a nuisance alarm because it disrupts normal activities without serving the intended safety function of alerting occupants to danger.

The other options, such as smoke from cooking or a power outage affecting alarms, also present scenarios that can lead to alarms being triggered, but they do not specifically represent nuisance alarms in the way that a direct mechanical failure of equipment does. Smoke from cooking may activate alarms as a warning signal, while a power outage affects the system's functionality rather than being a fault within the alarm itself. Malfunction of a sprinkler system, while potentially problematic, typically does not fall under the category of nuisance alarms in the same way that a failure of a smoke detector would. Consequently, the mechanical failure of a smoke detector is the most appropriate example of a nuisance alarm.