**Core Concept**
The question tests the understanding of serological diagnosis in various infectious diseases, focusing on the role of antibody detection in diagnosing these conditions. Serology is a crucial diagnostic tool in many infections, including bacterial, viral, and parasitic diseases.

**Why the Correct Answer is Right**
The correct answer, **Syphilis**, is diagnosed serologically using tests like the Rapid Plasma Reagin (RPR) and the Treponema Pallidum Particle Agglutination Assay (TPPA), which detect antibodies against the bacterium *Treponema pallidum*. This method is highly specific and sensitive for diagnosing syphilis in its various stages.

**Why Each Wrong Option is Incorrect**
**Option A:** Actinomycosis is typically diagnosed through microbiological culture or histopathological examination of affected tissues, rather than serology.
**Option B:** Tuberculosis (T.B.) diagnosis often involves microbiological confirmation through sputum smear, culture, or molecular tests, and while there are serological tests, they are not the primary diagnostic method.
**Option D:** Gonorrhoea is usually diagnosed by nucleic acid amplification tests (NAATs) or culture, not serology.
**Option E:** Q fever can be diagnosed serologically, but the question seeks the most appropriate answer among the options given, and syphilis is more classically associated with serological diagnosis.

**Clinical Pearl / High-Yield Fact**
Syphilis is a classic example where serological tests are the cornerstone of diagnosis, given the bacterium's fastidious nature and the disease's various stages requiring different management approaches.

**Correct Answer:** C. Syphilis