**Core Concept**
The question is testing the common causes of unilateral (U/L) mucopurulent rhinorrhoea in children, which is often a sign of acute bacterial sinusitis. The underlying principle is the anatomy of the nasal passages and sinuses in children, and the common pathogens that cause sinusitis.

**Why the Correct Answer is Right**
The correct answer is adenoiditis. Adenoids are lymphoid tissues located in the nasopharynx, and in children, they are a common site for infection. When adenoids become infected, it can lead to the spread of infection to the surrounding sinuses, causing mucopurulent rhinorrhoea. The Eustachian tube, which connects the middle ear to the nasopharynx, is shorter and more horizontal in children, making it easier for pathogens to ascend and cause infection.

**Why Each Wrong Option is Incorrect**
**Option A:**
This option is incorrect because otitis media is an infection of the middle ear, and while it can be associated with sinusitis, it is not the primary cause of unilateral mucopurulent rhinorrhoea.

**Option B:**
This option is incorrect because viral upper respiratory tract infections are common in children, but they typically do not cause mucopurulent rhinorrhoea.

**Option C:**
This option is incorrect because allergic rhinitis can cause nasal congestion and rhinorrhoea, but it is typically bilateral and not mucopurulent.

**Clinical Pearl / High-Yield Fact**
In children, unilateral mucopurulent rhinorrhoea is often a sign of acute bacterial sinusitis, and adenoiditis is a common underlying cause. It's essential to consider this diagnosis in children with recurrent or persistent sinusitis.

**Correct Answer: A. Adenoiditis**