Which of the following statements are correct?
i. Indifference curve is upward sloping
ii. Indifference curve is convex to the origin.
iii. MRS is the slope of indifference curve.
iv. MRSxy diminishes as the quantity of X increases.

ii, iii, iv

Marginal Rate of Substitution (MRS) is the slope of indifference curve. MRS keeps on diminishing as X increases because as X increases and Y decreases, the utility from X diminishes and that from Y increases. As a result, consumer is willing to give up less and less units of Y to obtain more units of X. And since MRS keeps on diminishing, indifference curve is convex to the origin. Hence, statement ii, iii and iv are correct.