Why indifference curves are convex to origin?

The correct answer is Option (4) → Due to a diminishing marginal rate of substitution.

Indifference curves are convex to the origin because of the Law of Diminishing Marginal Rate of Substitution (MRS), which states: As a consumer substitutes one good (say, Good X) for another (Good Y), the amount of Good Y they are willing to give up decreases with each additional unit of Good X.

This results in a declining MRS, causing the curve to bend inward (i.e., be convex to the origin).