Introduction:
In this scenario, we are given three samples of juices, namely A, B, and C, which contain glucose as the only sugar present in them. The concentrations of these samples are 0.1M, 0.5M, and 0.2M respectively. We are asked to determine which fruit juice will have the highest freezing point.

Explanation:
To determine the freezing point of a solution, we need to consider the concept of freezing point depression, which states that the presence of a solute in a solvent lowers the freezing point of the solvent. In this case, the solute is glucose, and the solvent is the fruit juice.

Freezing point depression:
The freezing point depression of a solution can be calculated using the formula:
ΔTf = Kf * m

Where:
ΔTf is the freezing point depression
Kf is the cryoscopic constant (a characteristic property of the solvent)
m is the molality of the solution (moles of solute per kilogram of solvent)

Here, we have the concentrations of the samples in terms of molarity (moles of solute per liter of solution), so we need to convert them to molality before comparing their freezing points.

Calculating molality:
To convert molarity to molality, we need to know the density of the solutions. Assuming the densities of the three juices are equal, we can use the formula:
m = (M * 1000) / (density * MW)

Where:
m is the molality
M is the molarity
density is the density of the solution
MW is the molecular weight of glucose

Comparing freezing points:
Once we have the molality values for each sample, we can compare their freezing points. The freezing point depression is directly proportional to the molality of the solution. Therefore, the sample with the highest molality (or concentration) of glucose will have the highest freezing point depression and, consequently, the lowest freezing point.

Conclusion:
Based on the given concentrations, sample B with a concentration of 0.5M will have the highest freezing point. This is because it has the highest molality of glucose among the three samples. Samples A and C will have lower freezing points compared to sample B, but their freezing points will be the same since they have the same molality of glucose. Therefore, the correct answer is option b) B.