Euler's formula is a widely used formula in structural engineering to determine the critical buckling load of a column. It relates the critical buckling load to the material properties and geometric properties of the column. However, this formula is not valid for all cases, and there are certain conditions under which it may not hold true. One such condition is the slenderness ratio of the column.

The slenderness ratio (λ) of a column is defined as the ratio of its effective length (l) to its least radius of gyration (r). It is a measure of how slender or stocky a column is, and it determines the column's tendency to buckle under compressive loads. The slenderness ratio is given by the formula:

λ = l / r

where l is the effective length of the column and r is the least radius of gyration.

When the slenderness ratio exceeds a certain critical value, the Euler's formula becomes invalid, and the column may not buckle in the predicted manner. This critical value of the slenderness ratio depends on the boundary conditions and the end fixity of the column.

In the case of a mild steel column, the critical slenderness ratio is generally taken as 60. This means that if the slenderness ratio of a mild steel column exceeds 60, the Euler's formula cannot be used to accurately determine the critical buckling load.

Hence, in the given question, the correct answer is option 'A' - 60.