A

Step 1: Understand mutual inductance between two coils, which depends on the alignment of their axes.
Step 2: The mutual inductance, M, is given by the formula \( M = k \sqrt{L_1 L_2} \), where k is the coupling coefficient, and L_1 and L_2 are the self-inductances of the coils.
Step 3: The coupling coefficient k depends on the angle between the coils. It is maximum (k=1) when the coils are perfectly aligned or parallel.
Step 4: If the axes are perpendicular (Option D), k=0, leading to no mutual inductance. For other angles like 45 degrees (Option C) or 60 degrees (Option B), the value of k will be less than 1 but greater than 0.
Step 5: Thus, the mutual inductance is maximized when the coils are parallel (Option A).
Therefore, the correct answer is A.