**Core Concept**
The child's presentation of fever, altered sensorium, and purpuric rashes, along with hypotension, is suggestive of a severe infection, likely meningococcemia, a condition caused by Neisseria meningitidis. This bacterium can lead to septic shock, characterized by hypotension, and disseminated intravascular coagulation (DIC), which results in purpuric rashes.

**Why the Correct Answer is Right**
The treatment of choice in this scenario is intravenous antibiotics, specifically ceftriaxone, which covers Neisseria meningitidis. Ceftriaxone is a third-generation cephalosporin with broad-spectrum activity against Gram-negative bacteria, including Neisseria species. It acts by inhibiting cell wall synthesis, ultimately leading to bacterial lysis and death. Additionally, administration of ceftriaxone should be accompanied by supportive measures, such as fluid resuscitation and vasopressors, to manage hypotension and maintain circulatory stability.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is likely incorrect because it does not specify the antibiotic or dosing regimen required for effective treatment of meningococcemia.
**Option B:** This option may be incorrect because it does not address the need for supportive care, such as fluid resuscitation and vasopressors, which are essential in managing septic shock.
**Option C:** This option is incorrect because it does not provide a specific antibiotic regimen, and the use of a combination of antibiotics may not be necessary in this case.

**Clinical Pearl / High-Yield Fact**
Meningococcemia is a medical emergency that requires prompt recognition and treatment. The classic triad of fever, rash, and hypotension is often seen in this condition, and administration of antibiotics should not be delayed.

**Correct Answer:** C. Ceftriaxone 100 mg/kg IV daily in two or three divided doses, in addition to supportive care.