**Column with Maximum Equivalent Length**
The correct answer to the question is option 'd' - one end fixed and the other end free. Let's understand why this is the correct answer.

**Introduction to Columns**
In structural engineering, a column is a vertical structural member designed to support compressive loads. Columns are critical elements in many structures, such as buildings, bridges, and towers. They are subjected to axial compressive forces that act along their length.

**Column Buckling**
When a column is subjected to a compressive load, it tends to buckle or deform laterally. Buckling occurs when the applied load exceeds the critical buckling load, causing the column to bend and lose its stability. Buckling can result in catastrophic failure of the column and the entire structure.

**Effective Length Factor**
The effective length factor (K) is used to determine the buckling behavior of a column. It takes into account the boundary conditions at the ends of the column and affects the critical buckling load. The value of K depends on the support conditions at the column ends.

**Different Support Conditions**
Let's consider the different support conditions for column ends:

1. Both Ends Hinged (Pinned): In this case, both ends of the column are free to rotate, allowing the column to buckle easily. The effective length factor for this condition is K = 1.0.

2. Both Ends Fixed: When both ends of the column are fixed, they are restrained against rotation. This significantly increases the column's resistance to buckling. The effective length factor for this condition is K = 0.5.

3. One End Fixed and the Other End Hinged: This condition provides partial restraint to the column against rotation. The effective length factor for this condition is K = 0.7.

4. One End Fixed and the Other End Free: This condition provides partial restraint at one end and allows rotation at the other end. The effective length factor for this condition is K = 2.0.

**Explanation of the Answer**
The maximum equivalent length occurs when one end of the column is fixed and the other end is free. In this condition, the effective length factor (K) is 2.0, which is greater than any other support condition. A higher effective length factor leads to a lower critical buckling load, making the column more susceptible to buckling.

In practical terms, a column with one end fixed and the other end free has the highest risk of buckling and requires additional design considerations to ensure its stability. The fixed end provides some resistance against buckling, while the free end allows for lateral deformations.

Therefore, option 'd' - one end fixed and the other end free - is the correct answer as it represents the column with the maximum equivalent length.