**Core Concept**
Diagnostic tests for extra-intestinal invasive amoebiasis aim to detect the presence of the amoeba *Entamoeba histolytica* or its antigens/excretions in tissues or bodily fluids outside the gastrointestinal tract. This is crucial for diagnosing conditions such as amoebic liver abscess, which requires prompt treatment to prevent complications.

**Why the Correct Answer is Right**
The correct answer is **C. Serological tests**. Serological tests, including indirect hemagglutination (IHA), enzyme-linked immunosorbent assay (ELISA), and complement fixation (CF), measure the presence of antibodies against *E. histolytica* in the patient's serum. These tests are useful for diagnosing extra-intestinal invasive amoebiasis, particularly amoebic liver abscess, as they can detect antibodies in the blood that have been produced in response to the amoeba.

**Why Each Wrong Option is Incorrect**
* **Option A:** Direct fluorescent antibody (DFA) tests are useful for detecting *E. histolytica* antigens in stool samples, but they are not the best diagnostic tool for extra-intestinal invasive amoebiasis.
* **Option B:** Stool culture is not a reliable method for diagnosing extra-intestinal invasive amoebiasis, as the amoeba may not be present in the stool.

**Clinical Pearl / High-Yield Fact**
The presence of antibodies against *E. histolytica* in the serum can persist for several years after the initial infection, making serological tests useful for diagnosing past exposure to the amoeba.

**Correct Answer:** C. Serological tests.