A

Step 1: Given the expression for the strong nuclear force:\
F = \frac{Ce^{-kr}}{r^2}\

Step 2: We need to find the dimensions of C, k, and r.\
Let the dimensions be as follows: C has dimensions [C], k has dimensions [k], and r has dimensions [L].\
According to the equation of force F, the dimensions of force are [F] = \[M L T^{-2}\]
\
Step 3: Substituting dimensions in the force equation:
\[M L T^{-2} = \frac{[C] e^{-kr}}{L^2}\]

Step 4: Since e^{-kr} is dimensionless, [kr] is dimensionless, implying [k] * [L] = 1, thus [k] = [L^{-1}].\
Substituting the dimensions of k into the force equation gives:
\[M L T^{-2} = \frac{[C]}{L^2}\]

Step 5: Rearranging gives dimensions of C:
\[C = M L^3 T^{-2}]\

Step 6: Therefore, the dimensions of C, k, and r are:
[C] = M L^3 T^{-2}, [k] = L^{-1}, [r] = L.
So, the correct answer is A.