**Core Concept**
The underlying principle being tested is the approach to diagnosing the cause of convulsions in a premature baby, focusing on the most critical and immediate potential causes that require urgent intervention. **Hypoglycemia**, **hypocalcemia**, and **infection** are common concerns, but given the context of a premature baby and the timing, **metabolic disturbances** and **neonatal hypoglycemia** are particularly relevant.

**Why the Correct Answer is Right**
Given the scenario of a premature baby with convulsions after 2 days of birth, the first investigation should aim at identifying potentially life-threatening conditions that can cause seizures, such as **hypoglycemia**. Checking the blood glucose level is a rapid, straightforward test that can quickly identify if the baby's seizures are due to low blood sugar, a condition that requires immediate correction to prevent further brain injury.

**Why Each Wrong Option is Incorrect**
**Option A:** Without the specific details of option A, we cannot directly address its inaccuracies, but typically, other options might include imaging studies or more complex metabolic tests that, while important, do not take precedence over a simple, critical test like blood glucose in the initial assessment of a seizing premature infant.
**Option C:** Similarly, without specifics, if this option involves a less immediately critical test or one that does not directly address a potentially rapid-onset, reversible cause of seizures like hypoglycemia, it would be incorrect as the first line.
**Option D:** Again, lacking details, if this option suggests a test that is not as directly relevant to the acute management of seizures in a premature infant as a blood glucose test, it would be an inappropriate first choice.

**Clinical Pearl / High-Yield Fact**
In neonates, especially premature babies, **hypoglycemia** is a critical condition that can present with nonspecific symptoms, including seizures. It is essential to quickly identify and treat hypoglycemia to prevent long-term neurological damage. A key point to remember is that seizures in the neonatal period, particularly in premature infants, warrant an immediate check of blood glucose levels among other critical assessments.

**Correct Answer:** Correct Answer: D. Blood glucose.