**Core Concept:**
The question is about a patient presenting with a femoral fracture and developing breathlessness on the 3rd day of admission. We need to identify the most probable diagnosis based on the given information.

**Why the Correct Answer is Right:**
The correct answer, **Option C: Pulmonary Oedema**, is related to the development of breathlessness in a patient with a femoral fracture. Pulmonary oedema occurs when there is an excess accumulation of fluid in the lungs, leading to impaired gas exchange and shortness of breath. In this scenario, the patient has a fracture, which may result in immobilization, leading to muscle inactivity and decreased cardiac output. This can lead to a decrease in preload and decreased cardiac output, which could potentially cause pulmonary oedema due to reduced cardiac output and decreased cardiac filling pressure.

**Why Each Wrong Option is Incorrect:**
Option A: **Acute Pulmonary Embolism (APE)** is caused by the sudden blockage of pulmonary arteries by a blood clot and can present with sudden onset of breathlessness. This is not the correct answer because the patient has developed breathlessness on the 3rd day of admission, which is a gradual onset.

Option B: **Acute Pulmonary Infarction (API)** is caused by a sudden occlusion of a pulmonary artery branch and can present with sudden onset of breathlessness. This is not the correct answer because the patient has developed breathlessness on the 3rd day of admission, which is a gradual onset.

Option D: **Acute Myocardial Infarction (AMI)** is caused by an acute coronary occlusion leading to acute myocardial necrosis and can present with sudden onset of chest pain and breathlessness. This is not the correct answer because the patient has developed breathlessness on the 3rd day of admission, which is a gradual onset.

**Clinical Pearl or High-Yield Fact:**
Patients with femoral fractures often require immobilization, which can lead to decreased cardiac output and reduced cardiac filling pressure. This can potentially cause pulmonary oedema as a complication. In this case, the patient presents with breathlessness on the 3rd day of admission, which is a gradual onset.

**Explanation:**
The correct answer, **Option C: Pulmonary Oedema**, is the most plausible diagnosis given the gradual onset of breathlessness in a patient with a femoral fracture. Pulmonary oedema occurs due to reduced cardiac output and decreased cardiac filling pressure, which can lead to the accumulation of fluid in the lungs, causing shortness of breath. The other options (APE, API, and AMI) are incorrect because they present with sudden onset symptoms, which is inconsistent with the gradual onset of breathlessness in this case.