**Core Concept**
Pancreatic carcinoma is a malignant tumor of the pancreas, and early detection is crucial for improving survival rates. The sensitivity of an investigation refers to its ability to detect the disease when it is present, and in this context, we are looking for the most sensitive test for pancreatic carcinoma.

**Why the Correct Answer is Right**
The most sensitive investigation for pancreatic carcinoma is the **Imaging with Endoscopic Ultrasound (EUS)**. EUS combines endoscopy and ultrasound to provide high-resolution images of the pancreas and surrounding tissues. It allows for precise visualization of small pancreatic lesions, even in the early stages of the disease. This is because EUS can detect changes in the pancreas as small as 5 mm in diameter, which is much smaller than what other imaging modalities like CT scans or MRI can detect.

**Why Each Wrong Option is Incorrect**
**Option A:** **CT Scan with Contrast**. While CT scans are commonly used to detect pancreatic carcinoma, they have a lower sensitivity for small lesions and may not detect the disease in its early stages.
**Option B:** **MRI with Contrast**. MRI is not as sensitive as EUS for detecting pancreatic lesions, especially in the early stages of the disease.
**Option C:** **Endoscopic Retrograde Cholangiopancreatography (ERCP)**. ERCP is primarily used for diagnosing and treating bile duct and pancreatic duct disorders, but it is not as sensitive as EUS for detecting pancreatic carcinoma.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that EUS is not only the most sensitive investigation for pancreatic carcinoma but also provides a safe and minimally invasive way to obtain tissue samples for histopathological examination.

**Correct Answer:** C.