Which of the following is a sign of meningitis in a child?

A stiff neck is indeed a classic sign of meningitis in children. This occurs because the inflammation of the protective membranes covering the brain and spinal cord can lead to increased rigidity in the neck muscles. When a child has meningitis, the body's protective response can manifest as muscle stiffness, making it painful and difficult for them to move their neck, especially when trying to look down. Thus, the presence of neck stiffness, especially when combined with other symptoms like fever or sensitivity to light, is a critical indicator for diagnosing meningitis.

While fever can be present in various infections and is a common sign of illness in children, it alone is not specific enough to indicate meningitis. Similarly, while rashes can occur with some types of meningitis (such as meningococcal meningitis), they are not as definitive as a stiff neck. A cough typically relates to respiratory infections and is not associated with meningitis. Therefore, the specific sign of a stiff neck makes it the most relevant indicator of meningitis in this context.