Question

Rank from non-polar to polar:
β-carotene, chlorophyll A, and lycopene

Answer 1

You'd want to look at the structures (which im sure you already have) and identify the functional groups present.

The hardest to differentiate from is beta carotene and lycopene; in general double bonds are more polar than single bonds, so you could use that as a guideline - but overall structure (i.e. symmetry) influences polarity.

Lycopene is more soluble in hexanes (organic, non-polar solvent) than beta carotene (i looked this up), so you would expect it to be less polar, but the ends of beta carotene are rings with only single bonds and from that feature i would expect it to be less polar.

Polarity is most often judged by solubility, on that alone, Lycophene is more non-polar.