Given 100 features, you have to select 10 features for a 3 class classification problem. What is your approach?

Would be helpful if someone helps me solving this.

Can you give some more background on where this question arises?

I would say it’s rather theoretical, so from that perspective, I would perform a PCA , getting 10 strongest factors that express maximum variation (i.e., there is the most variability in terms of values among each dimension/feature).
3 - class classification task is a bit indifferent to the dimensionality reduction.

This is my opinion, surely there are hundreds of other approaches!