It is common to mix polar solvents (e. g., acetone) with non-polar solvents (e. g., hexane) to obtain an eluting solvent of intermediate polarity. Would it be appropriate to use a water-DMSO mixture

No, it is not appropriate to mix water and DMSO

Explanation:

We have to realize that DMSO is a highly polar solvent and water is a highly polar solvent. The question explicitly says that our target is to produce a solvent of intermediate polarity.

We can only do this by mixing a polar and a nonpolar solvent. We have been given the example of the mixture of acetone/hexane which is quite a perfect mixture.

Thus, it is inappropriate to mix DMSO and water.

explanation: no but i do not usually comment