Indifference curve is a curve that shows consumption bundles that give the consumer the same level of satisfaction. Indifference map, on the other hand Indifference curve is a graph of two or more indifference curves.

two indifference curve never cut each other..

a single indifference curve cannot cross itself.

what will be the shape of indifference curve if one of the two goods is a free commodity

The three major characteristics of an indifference curve are:

1. They are negatively sloped

2. They are convex to the origin

3. Indifference curve cannot be intersected