**Core Concept:** Clearance (C) is a pharmacokinetic parameter that represents the rate at which a substance is eliminated from the body. It is calculated as the ratio of the volume of distribution (Vd) to the elimination rate constant (Ke).

**Why the Correct Answer is Right:** The clearance (C) can be calculated using the formula:

C = Vd / Ke

In this scenario, we are given the concentration of the substance in plasma (Cp) and urine (Cu), as well as the urine flow rate (Uf). We can rearrange the formula to solve for the volume of distribution (Vd):

Vd = Cp * Uf / Cu

Given: Cp = 10 mg%, Cu = 100 mg%, and Uf = 2 ml/min

Vd = (10 mg%) * (2 ml/min) / (100 mg%)

Now, we need to find the elimination rate constant (Ke). The elimination rate constant is the inverse of the half-life (t1/2), which can be calculated using the formula:

t1/2 = ln(2) / Ke

First, we need to find Ke:

Ke = ln(2) / t1/2

Given: t1/2 is unknown, but we know that:

ln(2) = ln(2) / Ke

Solving for Ke:

Ke = ln(2) / t1/2

**Why Each Wrong Option is Incorrect:**

A. This option is incorrect because we cannot solve for Ke directly from the given information. We need more information about the substance's half-life (t1/2) to find Ke.

B. This option is incorrect because the formula for Ke is derived from the t1/2 formula but does not provide enough information to solve for Ke.

C. This option is incorrect because it only provides a numerical value for Vd but does not address the problem of finding Ke.

D. This option is incorrect because it relies on the incorrect assumption that Ke can be directly calculated from the given information. We need to find t1/2 first to solve for Ke.

**Clinical Pearl:** The concept of half-life (t1/2) is crucial in pharmacokinetic calculations. In this case, the half-life would be:

t1/2 = ln(2) / Ke

To find Ke, we need additional information about the substance's half-life.