During which method of separation is one of the components of the mixture lost?

a) distillation
b) magnetic separation
c) screening
d) evaporation

I am quite confused with your question. You are asking about the method of separation wherein one of the components is 'lost'. However, these methods are only physical changes that separates components of the mixtures. But nothing gets lost according to the Law of Conservation of Mass. The components are separated but both can still be recovered.

In distillation, the more volatile component vaporizes and allowed to condense again to gather the volatile-rich solution. The less volatile stays on the bottoms of the tower. In magnetic separation, you just collect the metals from non-metals. In screening, you separate the smaller pieces from the larger pieces with the use of screens. In evaporation, water is separated from the solute by vaporizing it. You will be left with a more concentrated solution. However, the water is not lost because it could be condensed again back to liquid water.

However, to provide an answer, I think the closest would be evaporation. This applies to natural evaporation like a cup of coffee left in open air. You can't recover water anymore because it evaporized to the atmosphere. But still, technically, it comes back as precipitated rain.