Statement I : Limiting friction depends on surface area.

Statement II : Kinetic friction depends on surface area.

The correct option is Both statements are false.

Let us understand the dependency of friction on the surface area of contact:
Frictional force, whether limiting static friction ($f_s$) or kinetic friction ($f_k$), is mathematically expressed as:
$f_s={\mu }_{s}N$
and
$f_k={\mu }_{k}N$
where ${\mu }_s$ is the coefficient of static friction, ${\mu }_k$ is the coefficient of kinetic friction, and $N$ is the normal contact force.

1. Independence of Surface Area:
The force of friction depends on the nature of the materials in contact and the normal force pressing the surfaces together. It does not depend on the apparent area of contact.
At a microscopic level, surfaces are rough and touch only at certain points (microscopic contact points). When the apparent area of contact increases, the normal force is distributed over a larger area, which decreases the pressure at individual contact points. Conversely, if the apparent area decreases, the pressure increases. As a result, the actual microscopic area of contact remains proportional to the normal force and is independent of the apparent area. Thus, the overall frictional force remains unchanged.

2. Evaluation of the Statements:
- Statement I: "Limiting friction depends on surface area" is false because limiting static friction is independent of the apparent area of contact.
- Statement II: "Kinetic friction depends on surface area" is also false because kinetic friction is independent of the apparent area of contact.

Therefore, both Statement I and Statement II are false.