Let's evaluate each mixture and its appropriate separation method:
- A. CHCl\(_3\) + C\(_6\)H\(_5\)NH\(_2\) (Chloroform and Aniline): Fractional distillation is suitable for separating chloroform and aniline due to their differing boiling points. Therefore, A corresponds to III.
- B. Crude oil + petroleum industry: Simple distillation, based on boiling point differences, is employed to separate crude oil components, a standard practice in the petroleum industry. Thus, B corresponds to IV.
- C. Glycerol from spent-lye: Steam distillation is utilized to separate glycerol from spent-lye, a technique for isolating water-soluble organic compounds. Hence, C corresponds to II.
- D. Aniline + water: Distillation under reduced pressure is appropriate for separating aniline and water, given aniline's significantly higher boiling point. This method is effective for components with substantial boiling point disparities. Consequently, D corresponds to I.
The correct pairing is (3) A-III, B-IV, C-II, D-I.