This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: No work is required to be done to move a test charge between any two points on an equipotential surface.
Statement 2: Electric lines of force at the equipotential surfaces are mutually perpendicular to each other.

Let us understand both statements step by step.

Starting with Statement 1: "No work is required to be done to move a test charge between any two points on an equipotential surface."

An equipotential surface is a surface where every point has the same electric potential. This means that for any two points A and B on such a surface, the potential difference between them is zero: $$ V_A - V_B = 0 $$ or $$ \Delta V = 0 $$.

The work done by the electric field when moving a test charge q from point A to point B is given by the formula: $$ W = -q \Delta V $$. Since $$ \Delta V = 0 $$, we have: $$ W = -q \times 0 = 0 $$.

This means the electric field does zero work. If we consider an external agent moving the charge slowly (without changing its kinetic energy), the work done by the external agent must counteract the work done by the field. Since the field does zero work, the external agent also does zero work. Therefore, Statement 1 is true.

Now, Statement 2: "Electric lines of force at the equipotential surfaces are mutually perpendicular to each other."

Electric lines of force are the same as electric field lines. We know that electric field lines are always perpendicular to equipotential surfaces. This is because if the electric field had a component tangent to the surface, it would cause a potential difference along the surface, violating the equipotential condition. However, Statement 2 claims that the field lines are mutually perpendicular to each other.

Mutually perpendicular means that the field lines intersect at right angles to one another. But at any given point on an equipotential surface, there is only one electric field direction (normal to the surface). Field lines cannot be mutually perpendicular at a point because only one line passes through each point. Moreover, when considering the entire surface, field lines are not necessarily perpendicular to each other.

For example, near a point charge, equipotential surfaces are spheres. The electric field lines are radial and diverge from the charge. They are not mutually perpendicular; instead, they are all directed radially outward or inward. In a uniform electric field, equipotential surfaces are planes, and field lines are parallel straight lines, which are not perpendicular to each other. Therefore, Statement 2 is false.

Since Statement 1 is true and Statement 2 is false, the correct choice is Option C.

Hence, the correct answer is Option C.