Question

Why is ray florets of sunflower called neuter flower?

Answer 1

The ray florets of sunflower are called neuter flower because it contains neither male or female parts. 

Any of the small strap-shaped flowers in the flower head of certain composite plants, such as the daisy is called Ray floret.
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Answer 2

Ray florets, contrary to disc florets in the center, are petal like structures that bear the outer ring of the flower. Ray florets are called neuter because they are sterile and do not produce seeds like disc florets. Both stamen and pistil, i.e. male and female sex organs are missing in ray florets, hence making it sterile.