A homogeneous mixture consists of 34% ethanol and 66% isopropanol. Which of these is the solute of the mixture?

The solute is ethanol. This is a matter of looking at the definition of solute. Solute - The minor component in a solution. What's dissolved in the solvent. With that definition in mind, the answer is pretty obvious. The solute is the 34% ethanol. It loses on any basis you can imagine for comparison. Percentage wise it's about half that of the isopropanol. Their densities are almost identical 789 kg/m^3 vs 786 kg/m^3, so there's still almost twice as much isopropanol as ethanol by mass.