**Core Concept**
Diabetic ketoacidosis (DKA) is a serious complication of diabetes characterized by hyperglycemia, metabolic acidosis, and the presence of ketones in the blood. The diagnosis of DKA involves assessing the severity of hyperglycemia, the degree of acidosis, and the presence of ketones.

**Why the Correct Answer is Right**
The most useful investigation in the diagnosis of DKA is the arterial blood gas (ABG) analysis. This test measures the pH, pCO2, and bicarbonate levels in the blood, providing information on the severity of acidosis. Additionally, the ABG can help identify the underlying cause of the acidosis, such as diabetic ketoacidosis or lactic acidosis. The presence of ketones in the blood can be confirmed using a ketone strip or a blood gas analyzer.

**Why Each Wrong Option is Incorrect**
**Option A:** Fasting blood glucose is a useful test for diagnosing DKA, but it does not provide information on the severity of acidosis or the presence of ketones. While it can confirm hyperglycemia, it is not the most useful investigation in the diagnosis of DKA.

**Option B:** Urine ketone testing can detect the presence of ketones in the urine, but it is not as sensitive as blood gas analysis. Additionally, urine ketone testing may not detect ketones in the early stages of DKA.

**Option C:** Serum electrolyte levels are important in the management of DKA, but they are not the most useful investigation in the diagnosis of DKA.

**Clinical Pearl / High-Yield Fact**
In the diagnosis of DKA, it is essential to remember that the presence of ketones in the blood and urine is a critical factor. The ratio of ketones to glucose in the blood can help differentiate DKA from other causes of metabolic acidosis.

**Correct Answer: A. Arterial blood gas analysis. Arterial blood gas (ABG) analysis is the most useful investigation in the diagnosis of diabetic ketoacidosis.**