The study of rudimentary organs is

• The study of vestigial organs is known as Dysteleology. Vestigial organs are also referred to as rudimentary organs. 
• The term dysteleology implies the investigation of something inconsequential or has no reason for the existence of the organism. 
• Vestigial organs are those organs of our body that used to be functional for our ancestors however presently they don't have a lot of direction in our body and with time their size has reduced because of less utilization.
• Study of skin is called Dermatology.
• Study of hands is called Chirology.
• Study of causes of diseases/illness is called Etiology.

Hence, option B is the correct answer.