The correct answer is a) true.
Beta-carotene and chlorophyll a are indeed considered more non-polar largely due to the fewer functional groups containing oxygen in their molecular structures. Non-polar molecules tend to have lower electronegativity differences between their atoms, which in turn usually leads to a lack of polar functional groups. This is the case with beta-carotene and chlorophyll a, which are primarily hydrocarbons with fewer sites for hydrogen bonding.
On the other hand, xanthophyll and chlorophyll b have more functional groups that include oxygen, making them more polar. The presence of these polar functional groups increases their ability to interact with water and other polar solvents, hence, they are classified as more polar compared to their less functionalized counterparts.