**Core Concept**
The question is testing the clinical judgment of the student in selecting the least useful investigation for a patient with carcinoma rectum and a fixed mass, which suggests locally advanced disease. The underlying principle is the importance of staging and assessing the extent of cancer spread in determining the treatment plan.

**Why the Correct Answer is Right**
In this scenario, the patient has a fixed mass on a biopsy, indicating local spread of the cancer. Given the normal chest X-ray, there is no indication of distant metastasis to the lungs. The least useful investigation in this case would be a bone scan, as it is more relevant for detecting distant metastasis, which is unlikely given the normal chest X-ray and the presence of a fixed mass.

**Why Each Wrong Option is Incorrect**
**Option A:** CT scan of the abdomen and pelvis is useful for staging rectal cancer, as it can help identify local spread, distant metastasis, and involvement of adjacent organs.

**Option B:** MRI of the pelvis is also useful for rectal cancer staging, particularly for assessing the relationship between the tumor and the surrounding structures, such as the rectal wall and the pelvic nerves.

**Option C:** Endorectal ultrasound is a useful investigation for rectal cancer, as it can help identify the depth of tumor invasion and assess the involvement of the rectal wall.

**Clinical Pearl / High-Yield Fact**
In rectal cancer, a fixed mass on a biopsy suggests locally advanced disease, and the treatment plan should be adjusted accordingly. A normal chest X-ray does not rule out distant metastasis, and further investigations, such as a PET scan or a bone scan, may be necessary to assess the extent of cancer spread.

**Correct Answer:** D. Bone scan.