ANS:B - total reflux

The minimum number of theoretical plates required for achieving a given separation in a distillation column is when operating with total reflux. Total reflux means that all the liquid leaving the top of the column is returned back to the column as reflux. In this scenario, the liquid is continuously condensed and returned to the column without any of it being withdrawn as product. Total reflux maximizes the number of equilibrium stages in the column and allows for the most efficient separation achievable by the column design. When operating at total reflux, the number of theoretical plates required for a given separation is minimized because the process approaches ideal conditions, where there is essentially infinite contact between the vapor and liquid phases. This ensures that the composition of the vapor and liquid phases in each stage of the column closely matches the equilibrium composition, leading to maximum separation efficiency.