**Core Concept**
X-ray is the most sensitive investigation to detect minimal intraperitoneal free air, which is a hallmark of pneumoperitoneum. This is due to the high density difference between air and soft tissues, making it easily visible on radiographs.

**Why the Correct Answer is Right**
Free intraperitoneal air is usually the result of a perforation in the gastrointestinal tract. When air enters the peritoneal cavity, it accumulates in the dependent parts, such as the pelvis or the subdiaphragmatic space, where it is easily visible on a supine abdominal X-ray. The presence of free air is a medical emergency that requires prompt surgical intervention.

**Why Each Wrong Option is Incorrect**
**Option A:** CT scan is more sensitive than X-ray for detecting free air, but it is not the most sensitive investigation for minimal intraperitoneal free air. CT scan is more useful for detecting smaller amounts of free air and for localizing the source of the perforation.
**Option B:** Ultrasound is not typically used for detecting free air in the peritoneal cavity. While ultrasound can detect fluid collections and bowel wall thickening, it is not sensitive for detecting free air.
**Option C:** MRI is not typically used for detecting free air in the peritoneal cavity. MRI is more useful for detecting soft tissue injuries and infections.

**Clinical Pearl / High-Yield Fact**
A supine abdominal X-ray is the most sensitive investigation for detecting minimal intraperitoneal free air, particularly when the patient is lying on their back. The "cupola sign" or "pneumoperitoneum sign" is a classic radiographic finding of free air, where a crescent-shaped area of air is visible under the diaphragm.

**Correct Answer: A. X-ray**