Answer:
d) I and III only.
Step-by-step explanation:
Let be
and
the masses of the two laboratory carts and let suppose that
. The expressions for each kinetic energy are, respectively:
and
.
After some algebraic manipulation, the following relation is constructed:

Since
, then
. That is to say,
.
The expressions for each linear momentum are, respectively:
and

Since
, then
. Which proves that statement I is true.
According to the Impulse Theorem, the impulse needed by cart I is greater than impulse needed by cart II, which proves that statement II is false.
According to the Work-Energy Theorem, both carts need the same amount of work to stop them. Which proves that statement III is true.