**Core Concept**
The patient's presentation of acute renal failure and anuria suggests impaired renal function, and the normal ultrasound (USG) indicates that the renal structure is intact. Therefore, we need to assess renal function rather than structure.

**Why the Correct Answer is Right**
The best investigation to assess renal function in this scenario is the **Serum Creatinine and Urine Output (24-hour creatinine clearance)**. Serum creatinine levels can indicate the level of renal impairment, while 24-hour urine collection for creatinine clearance provides a more accurate assessment of renal function by estimating the glomerular filtration rate (GFR). This is because creatinine is freely filtered by the kidneys and is not significantly secreted or reabsorbed, making it an ideal marker for renal function.

**Why Each Wrong Option is Incorrect**
**Option A:** Serum Electrolytes - While electrolyte levels can provide some information about renal function, they are not a direct measure of renal function and can be influenced by various factors other than renal impairment.

**Option B:** Urine Analysis - Urine analysis can provide information about the presence of blood, protein, or casts in the urine, but it does not directly assess renal function.

**Option C:** Renal Biopsy - A renal biopsy is an invasive procedure that assesses renal structure and pathology, but it is not the best initial investigation for assessing renal function.

**Clinical Pearl / High-Yield Fact**
In patients with acute renal failure, it's essential to remember that the renal structure may be normal, and the primary issue lies in impaired renal function. Therefore, investigations should be focused on assessing renal function rather than structure.

**Correct Answer:** C. **Serum Creatinine and Urine Output (24-hour creatinine clearance)**