**Core Concept**
The investigation of choice for diagnosing carcinoma of the head of the pancreas involves imaging modalities that can provide detailed information about the pancreatic anatomy and surrounding structures. The head of the pancreas is a complex area with vital nearby structures, making it essential to use a modality that can accurately visualize this region.

**Why the Correct Answer is Right**
A CT scan is the most appropriate investigation for diagnosing carcinoma of the head of the pancreas. This is because CT scans can provide high-resolution images of the pancreas, surrounding tissues, and nearby vascular structures. The CT scan can also help identify any potential invasion of the tumor into adjacent structures, such as the portal vein or superior mesenteric vein. Additionally, CT scans can help assess the resectability of the tumor, which is crucial for surgical planning.

**Why Each Wrong Option is Incorrect**
* **Option A:** Hypotonic duodenogram is not a commonly used investigation for pancreatic carcinoma. This procedure involves injecting a contrast agent into the duodenum to visualize the duodenal anatomy, but it does not provide detailed information about the pancreas.
* **Option B:** X-ray abdomen is not sensitive enough to detect pancreatic carcinoma, especially in the early stages. X-rays are generally used for detecting bowel obstructions, kidney stones, or other abdominal emergencies.
* **Option C:** USG (ultrasound) can be used to evaluate the pancreas, but it is not the most effective modality for diagnosing carcinoma of the head of the pancreas. USG is operator-dependent and may not provide detailed information about the surrounding tissues.
* **Option D:** Endoscopy is useful for visualizing the luminal surface of the gastrointestinal tract, but it is not the primary investigation for diagnosing pancreatic carcinoma. Endoscopy can be used to obtain tissue samples for biopsy, but CT scans provide more comprehensive information about the tumor's extent.

**Clinical Pearl / High-Yield Fact**
When evaluating a patient with suspected pancreatic carcinoma, it is essential to use a multidisciplinary approach, including imaging, endoscopy, and tumor markers. A CT scan should be the primary imaging modality for diagnosing and staging pancreatic carcinoma.

**Correct Answer:** E. C.T. Scan