To determine the option with the correct spelling, let's examine each provided word:
paraphenalia: This spelling is incorrect. The correct spelling is "paraphernalia," which refers to miscellaneous articles, especially the equipment needed for a particular activity.
programe: This spelling is incorrect. The correct spelling is "program" in American English or "programme" in British English, meaning a planned series of events or performances.
pediatrics: This spelling is correct. "Pediatrics" refers to the branch of medicine that involves the medical care of infants, children, and adolescents. In British English, it can also be spelled "paediatrics."
beserk: This spelling is incorrect. The correct spelling is "berserk," which describes a state of frenzied or uncontrolled actions.