**Core Concept**
The initial investigation for carcinoma of the head of the pancreas involves a combination of imaging studies and laboratory tests to establish a diagnosis. The head of the pancreas is a critical area to evaluate, as it is closely related to the duodenum and the bile duct.

**Why the Correct Answer is Right**
The most appropriate initial method of investigation for carcinoma of the head of the pancreas is **Endoscopic Ultrasonography (EUS)**. EUS is a highly sensitive and specific imaging modality that provides high-resolution images of the pancreas, duodenum, and bile duct. It allows for accurate staging of the tumor, assessment of lymph node involvement, and evaluation of distant metastases. Additionally, EUS-guided fine-needle aspiration (FNA) can be performed to obtain tissue samples for histopathological examination.

**Why Each Wrong Option is Incorrect**
**Option A:** Computed Tomography (CT) scan is not the most appropriate initial investigation for carcinoma of the head of the pancreas, as it may not provide sufficient detail for accurate staging and assessment of lymph nodes.
**Option B:** Magnetic Resonance Imaging (MRI) may be useful in evaluating the extent of disease, but it is not as sensitive as EUS for detecting small pancreatic tumors.
**Option C:** Positron Emission Tomography (PET) scan is useful for evaluating distant metastases, but it is not the initial method of investigation for carcinoma of the head of the pancreas.

**Clinical Pearl / High-Yield Fact**
EUS is more sensitive than CT and MRI for detecting small pancreatic tumors, especially those located in the head and neck of the pancreas. It is also useful for guiding FNA, which can provide a definitive diagnosis.

**Correct Answer: C. EUS**