Which symptom is most associated with diabetes mellitus?

Polyuria is the correct answer because it refers to the condition of producing an abnormally large volume of urine, which is a classic symptom of diabetes mellitus. This occurs due to high blood glucose levels that lead to glucose spilling into the urine. The presence of glucose in the urine draws water with it through osmotic pressure, resulting in increased urine output.

Other symptoms associated with diabetes may include increased thirst and fatigue, but polyuria stands out as particularly indicative of the condition. The other options, while they could be related to other medical conditions or situations, are not specific or as commonly associated with diabetes mellitus. Dry skin may occur due to dehydration, and itchy eyes could result from various allergies or irritants, while headaches can be linked to numerous causes unrelated to diabetes. Thus, polyuria serves as a key indicator of diabetes due to its direct connection to the body's reaction to elevated glucose levels.