**Core Concept**
Neutrophilic leucocytosis refers to an increase in the number of neutrophils in the peripheral blood, often in response to acute inflammation, infection, or tissue damage. This condition is characterized by the release of stress hormones, such as adrenaline, and the subsequent mobilization of neutrophils from the bone marrow into the bloodstream.

**Why the Correct Answer is Right**
Hay fever, also known as allergic rhinitis, typically presents with eosinophilic leucocytosis, not neutrophilic leucocytosis. The inflammatory response in hay fever involves the release of histamine and other chemical mediators from mast cells, leading to the recruitment of eosinophils rather than neutrophils. This is in contrast to the other options, which are all associated with acute inflammation or infection, resulting in an increase in neutrophil count.

**Why Each Wrong Option is Incorrect**
**Option A:** Sepsis is a life-threatening condition characterized by a severe systemic inflammatory response to infection, often resulting in neutrophilic leucocytosis. Neutrophils play a crucial role in combating bacterial infections, and their numbers typically increase in response to sepsis.
**Option B:** Myocardial infarction, commonly known as a heart attack, triggers an acute inflammatory response, leading to the release of stress hormones and the mobilization of neutrophils into the bloodstream. This results in neutrophilic leucocytosis.
**Option C:** Pyogenic osteomyelitis, a type of bone infection, is characterized by an acute inflammatory response, which typically results in an increase in neutrophil count. Neutrophils are essential in combating bacterial infections in bone tissue.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that eosinophilic leucocytosis is often associated with allergic reactions, parasitic infections, and certain types of cancer, whereas neutrophilic leucocytosis is typically seen in bacterial infections, acute inflammation, and tissue damage.

**✓ Correct Answer: D. Hay fever**