**Core Concept**
Paraneoplastic syndromes are a group of systemic disorders caused by the production of substances by cancer cells, which can lead to various clinical manifestations. In the case of bronchogenic carcinoma, hypercalcemia is a well-known paraneoplastic syndrome caused by the secretion of parathyroid hormone-related protein (PTHrP) by the tumor.

**Why the Correct Answer is Right**
Hypercalcemia in bronchogenic carcinoma is primarily due to the production of PTHrP, which mimics the action of parathyroid hormone (PTH). PTHrP stimulates osteoclasts to break down bone, leading to the release of calcium into the bloodstream. This results in hypercalcemia, which can cause symptoms such as polyuria, abdominal pain, nausea, vomiting, and altered sensorium. The production of PTHrP is often seen in squamous cell carcinoma and small cell carcinoma of the lung.

**Why Each Wrong Option is Incorrect**
**Option A:** Hypokalemia is not directly associated with bronchogenic carcinoma. While electrolyte imbalances can occur in patients with cancer, hypokalemia is not a typical paraneoplastic syndrome associated with this condition.

**Option B:** Hyperkalemia is not a common electrolyte abnormality in bronchogenic carcinoma. The primary electrolyte abnormality in this condition is hypercalcemia, not hyperkalemia.

**Option C:** Hypocalcaemia is the opposite of what is typically seen in bronchogenic carcinoma. The production of PTHrP leads to an increase in calcium levels, not a decrease.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that hypercalcemia in cancer patients is often due to the production of PTHrP, and not just due to bone metastases. This distinction is crucial for diagnosing and managing paraneoplastic syndromes.

**Correct Answer Line**
✓ Correct Answer: D. Hypercalcemia