Solution:

To solve this problem, we need to understand the concept of isotonic solutions and how to calculate the molecular mass of glycerine.

Isotonic Solution:
An isotonic solution is a solution that has the same concentration of solutes as another solution. In this problem, we are given that a solution containing 10.2g glycerine per litre is isotonic with a 2% solution of glucose. This means that the concentration of glycerine in the solution is equivalent to the concentration of glucose in the 2% solution.

Calculating Concentration:
To calculate the concentration of glycerine in the solution, we need to convert the percentage of glucose to grams per litre. A 2% solution means that there are 2g of glucose in 100ml of solution. Therefore, we can calculate the concentration as follows:

(2g/100ml) * (1000ml/1L) = 20g/L

This means that the concentration of glycerine in the solution is 20g/L.

Calculating Molecular Mass:
Now, we can use the concentration of glycerine to calculate its molecular mass. The formula to calculate the molecular mass is:

Molecular Mass = (Concentration * Volume) / Number of Moles

In this case, the concentration is 10.2g/L and the volume is 1L. We also need to find the number of moles of glycerine.

To find the number of moles, we can use the formula:

Number of Moles = Mass of Glycerine / Molecular Mass of Glycerine

Substituting the given values, we have:

Number of Moles = 10.2g / Molecular Mass of Glycerine

Since the solution is isotonic, the concentration of glycerine is equal to the concentration of glucose, which is 20g/L. Therefore, we can write the equation:

10.2g / Molecular Mass of Glycerine = 20g/L

Simplifying the equation, we have:

Molecular Mass of Glycerine = 10.2g / 20g/L

Molecular Mass of Glycerine = 10.2g / (20g/1)

Molecular Mass of Glycerine = 10.2g * (1/20g)

Molecular Mass of Glycerine = 0.51g

Therefore, the molecular mass of glycerine is 0.51g.

Answer:
The correct option is (A) 91.8 g.