**Core Concept**
Pancreatic carcinoma is a malignancy of the pancreas, and its early detection is crucial for improving patient outcomes. The sensitivity of diagnostic investigations varies, and the most sensitive method is essential for timely diagnosis and treatment.

**Why the Correct Answer is Right**
The most sensitive investigation of pancreatic carcinoma is the Endoscopic Ultrasound (EUS). EUS combines endoscopy and ultrasound to provide high-resolution images of the pancreas and surrounding structures. It allows for the detection of small tumors and assessment of vascular invasion, making it an excellent tool for diagnosing pancreatic carcinoma. The proximity of the ultrasound probe to the pancreas and the ability to visualize the tumor in multiple planes contribute to its high sensitivity.

**Why Each Wrong Option is Incorrect**
**Option A:** CT scan is a sensitive investigation for pancreatic carcinoma, but it is not as sensitive as EUS, particularly for small tumors. CT scan provides information on the size and location of the tumor but may not detect early lesions.

**Option B:** MRI is a useful investigation for pancreatic carcinoma, especially for assessing vascular invasion and tumor extent. However, it is not as sensitive as EUS for detecting small tumors.

**Option C:** ERCP (Endoscopic Retrograde Cholangiopancreatography) is primarily used for therapeutic purposes, such as stenting, and is not the most sensitive investigation for pancreatic carcinoma.

**Clinical Pearl / High-Yield Fact**
EUS is particularly useful in the assessment of pancreatic masses, especially when CT or MRI findings are inconclusive. It is essential to consider EUS in the diagnostic algorithm for pancreatic carcinoma, particularly in patients with suspected pancreatic cancer.

**Correct Answer: A. Endoscopic Ultrasound (EUS).**