The marginal rate of substitution:?

Question

A.May rise or fall, depending on the slope of the budget line.
B.Rises as you move downward along an indifference curve.
C.Falls as you move downward along an indifference curve.
D.Remains the same along a budget line.

Answer 1

C. MRS is the slope of the indifference curve. The slope is considered to be negative and affected by a marginal diminishing returns.

As you have more of good x and less of good y you will be willing to give up less of good x to get more good y.

Answer 2

It depends from
1) how do you draw the curve (or how is its equation) and
2) semantics.

1- It's the same or changes?

Normally, indifference curves are draw curved, with a negative slope. So the rate of substitution is different at every point of the curve. (the slope is changing)

The rate remains the same only if the curve is a straight line. (I do not know any example of it, but...)

2- Rise or fall?

Normally you say that the rate of substitution of "Y" (in the "y" axis) vs X (represented in the "x" axis) is such and such

The rate is lower at every point: I would sacrifice less and less units of "Y" for every incremental unit of "X"

But nothing stops me from using the same chart to talk about the substitution of "X" vs. "Y".

In that case the rate of substitution of X vs Y is growing...I would sacrifice more and more units of "X" for one more unit of "Y"

Normally it is expressed as negative, but only by convention.
Beware of tricky questions...