**Core Concept**
The patient presented with fever, altered sensorium, and purpuric rash, indicating a severe systemic infection. The clinical presentation of purpura, particularly extensive palpable purpura, is suggestive of a vasculitic process, possibly associated with a bacterial infection.

**Why the Correct Answer is Right**
The patient's symptoms are consistent with Henoch-Schönlein purpura (HSP) nephritis, a complication of IgA vasculitis. The most common cause of HSP is infection with Group A beta-hemolytic Streptococcus (GABHS). In this context, the initial choice of antibiotic should target GABHS. **Ceftriaxone** is a broad-spectrum cephalosporin antibiotic effective against GABHS, making it an appropriate initial choice.

**Why Each Wrong Option is Incorrect**
* **Option A:** Although **Cefotaxime** is a third-generation cephalosporin effective against a broad spectrum of bacteria, it is not the first-line choice for GABHS infection.
* **Option B:** **Vancomycin** is effective against methicillin-resistant Staphylococcus aureus (MRSA) and other Gram-positive bacteria, but it is not the primary choice for GABHS infection.
* **Option D:** **Meropenem** is a carbapenem antibiotic effective against a broad spectrum of bacteria, including Gram-negative bacteria, but it is not the first-line choice for GABHS infection.

**Clinical Pearl / High-Yield Fact**
Henoch-Schönlein purpura (HSP) nephritis is a common complication of IgA vasculitis, often associated with a preceding GABHS infection. Prompt recognition and treatment of the underlying infection can prevent long-term renal damage.

**Correct Answer:** C. **Ceftriaxone**