**Core Concept**
The differential diagnosis for a woman with low-grade fever and bihilar adenopathy involves a range of infectious and non-infectious conditions. This presentation can be seen in diseases such as tuberculosis (TB), lymphoma, sarcoidosis, and histoplasmosis. The key is to identify the underlying cause of the adenopathy.

**Why the Correct Answer is Right**
The correct investigation to be useful in differential diagnosis is the **Histoplasma antigen test**. This test is used to diagnose histoplasmosis, a fungal infection that can cause bihilar adenopathy. The test detects the presence of Histoplasma capsulatum antigens in the urine or serum, which is a reliable indicator of infection.

**Why Each Wrong Option is Incorrect**
* **Option A:** The **Sputum AFB smear** is used to diagnose tuberculosis, which can also cause bihilar adenopathy. However, it may not be as sensitive as other tests and requires repeated samples for accurate results. This does not make it the least useful investigation.
* **Option B:** The **Sputum culture** is a gold standard for diagnosing tuberculosis, but it may take several weeks for results to become available. This does not make it the least useful investigation.
* **Option C:** The **CT scan of the chest** is a useful imaging modality for evaluating the extent of disease and identifying complications, but it is not a specific diagnostic test for the underlying cause of bihilar adenopathy.

**Clinical Pearl / High-Yield Fact**
When evaluating a patient with bihilar adenopathy, it's essential to consider both infectious and non-infectious causes. A thorough history, physical examination, and appropriate investigations are necessary to narrow down the differential diagnosis.

**Correct Answer:** C.