B

Step 1: Let's analyze each statement for correctness.

Statement (1): Centre of gravity (C.G.) of a body is the point at which the weight of the body acts.
- This statement is true. The center of gravity is indeed the point where the gravitational force can be considered to act.

Statement (2): Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius.
- This statement is true. As the distance from the Earth increases and we assume the Earth to be a point mass, the gravitational field becomes uniform, leading to the center of mass coinciding with the center of gravity.

Statement (3): To evaluate the gravitational field intensity due to anybody at an external point, the entire mass of the body can be considered to be concentrated at its C.G.
- This statement is also true for rigid bodies at large distances. The external gravitational field can be approximated by considering the mass to be concentrated at the C.G.

Statement (4): The radius of gyration of anybody rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis.
- This statement is false. The radius of gyration is defined as the distance from the axis of rotation, not just the perpendicular distance from the C.G. to the axis, but is calculated using the formula involving the moment of inertia.

Therefore, the pair of statements that are correct are (1) and (2) corresponding to Option B.