The correct option is D nocturnal and omnivorous
Cockroaches feed on all kinds of matter including food, paper, plastic, wires, cloth and even the dead bodies of their fellows (cannibalism). Hence they are omnivores.
They are active at night and rest during the day. Hence they are nocturnal creatures.
Organisms that consume plant products are known as herbivores and organisms that consume meat are known as carnivores.
Diurnal organisms are those that are active during the day and rest during the night.