Suppose there were plants that had a high concentration of Chlorophyll-$b$,but lacked Chlorophyll-$a$. Would they carry out photosynthesis? Then why do plants have Chlorophyll-$b$ and other accessory pigments?

(D) Chlorophyll-$a$ is the primary photosynthetic pigment and acts as the reaction center in both Photosystem-$I$ and Photosystem-$II$. It is the only pigment capable of converting light energy into chemical energy by emitting electrons during the light reaction.
Chlorophyll-$b$,carotenoids,and xanthophylls are accessory pigments. They absorb light energy at different wavelengths and transfer it to Chlorophyll-$a$,thereby increasing the efficiency of photosynthesis. Additionally,they protect the Chlorophyll-$a$ molecule from photo-oxidation.
If a plant lacks Chlorophyll-$a$,it cannot perform the primary photochemical reaction. Therefore,such a plant would not be able to carry out photosynthesis,even if it has a high concentration of Chlorophyll-$b$.