Indifference curves are graphical representations used in economics to analyze consumer preferences. They show different combinations of two goods that provide the same level of satisfaction or utility to the consumer. The axes used in drawing an indifference curve represent different variables, and the correct answer is option 'b', which states that quantities of two goods are taken on the axes while drawing an indifference curve.

Let's understand why option 'b' is the correct answer by breaking down the components of the other options:

a) Quantity along X axis and price along Y axis: This option refers to a typical demand curve, where the quantity demanded of a good is plotted on the X-axis, and the price of the good is plotted on the Y-axis. However, indifference curves do not consider prices but focus on the consumer's preferences for different combinations of goods.

c) Price of the two goods: Price is not a factor considered in indifference curves. These curves only represent the consumer's preferences for different combinations of goods, without taking into account the prices at which these goods are available.

d) Quantity and price of a good: While quantity is one of the variables considered in indifference curves, price is not. Indifference curves solely represent the different combinations of goods that yield the same level of satisfaction to the consumer.

Now, let's look at why option 'b' is the correct answer:

Quantities of two goods: Indifference curves are based on the consumer's preferences for different combinations of two goods. The quantities of these two goods are plotted on the X and Y axes of the graph. Each point on the indifference curve represents a specific combination of quantities, and all these combinations provide the consumer with the same level of satisfaction or utility.

For example, if we have two goods, A and B, the quantity of good A can be plotted on the X-axis, while the quantity of good B can be plotted on the Y-axis. The indifference curve represents the various combinations of quantities of A and B that give the consumer the same level of satisfaction. The shape of the indifference curve depends on the consumer's preferences, which can be expressed through indifference curves that are either convex or concave.

In conclusion, when drawing an indifference curve, the quantities of two goods are taken on the axes. This allows us to analyze the consumer's preferences and understand the combinations of goods that provide the same level of satisfaction.