Let's analyze both statements:

Statement (I): The limiting force of static friction depends on the area of contact and independent of materials.

This statement is incorrect. The limiting force of static friction does not depend on the area of contact but is dependent on the materials in contact. According to the law of static friction, the maximum static frictional force $$ f_s $$ that can occur before motion commences is given by the product of the coefficient of static friction $$ \mu_s $$ and the normal reaction force $$ N $$:

$$ f_s = \mu_s \times N $$

The coefficient $$ \mu_s $$ is a property that depends on the materials in contact, not on the area of contact. The normal force $$ N $$ is the force perpendicular to the surfaces in contact, influenced by the weight of the object and any other perpendicular forces acting upon it.

Statement (II): The limiting force of kinetic friction is independent of the area of contact and depends on materials.

This statement is correct. Once an object is in motion, the kinetic frictional force $$ f_k $$ opposing its motion is given by the product of the coefficient of kinetic friction $$ \mu_k $$ and the normal force $$ N $$:

$$ f_k = \mu_k \times N $$

The coefficient $$ \mu_k $$, like $$ \mu_s $$, is also a property dependent on the materials of the surfaces in contact. It generally has a lower value than $$ \mu_s $$, which is why objects tend to be easier to keep moving once they've started. The kinetic frictional force is independent of the area of contact between the two surfaces.

Given these explanations, the correct answer would be:

Option A: Statement I is incorrect but Statement II is correct.