**Core Concept**
Cystic fibrosis is a genetic disorder characterized by abnormal chloride transport across epithelial membranes, leading to thickened secretions and various systemic complications. The most sensitive investigation for diagnosing cystic fibrosis involves measuring the abnormal sweat electrolyte levels, particularly chloride.

**Why the Correct Answer is Right**
The sweat electrolyte test, also known as the sweat chloride test, is the primary diagnostic tool for cystic fibrosis. This test assesses the concentration of chloride ions in sweat, which is elevated in patients with cystic fibrosis due to the abnormal chloride transport mechanism. The sweat chloride test is considered the most sensitive investigation because it directly measures the underlying pathophysiological defect in cystic fibrosis. The test involves collecting a sweat sample, which is then analyzed for chloride content using a technique such as ion-selective electrode measurement.

**Why Each Wrong Option is Incorrect**
**Option A:** A CT scan is not a sensitive investigation for diagnosing cystic fibrosis. While it can provide information about lung structure and function, it is not specific for cystic fibrosis and may not detect the underlying genetic defect.
**Option B:** Ultrasound is not a suitable investigation for cystic fibrosis. While ultrasound can be used to assess lung structure and function, it is not sensitive or specific for diagnosing cystic fibrosis.
**Option D:** Tomogram is an outdated term that refers to a type of radiographic imaging. However, it is not a sensitive or specific investigation for diagnosing cystic fibrosis.

**Clinical Pearl / High-Yield Fact**
It's essential to note that the sweat chloride test is not diagnostic in isolation, and a diagnosis of cystic fibrosis should be confirmed through genetic testing. The sweat chloride test is a crucial screening tool, but it must be interpreted in the context of clinical symptoms and family history.

**✓ Correct Answer: C. Sweat electrolytes**