The excretory organ of a cockroach is the Malpighian tubules. Option 1, Nephridia, is incorrect. Nephridia are excretory structures found in some invertebrates such as annelids, not in cockroaches. Option 3, Malpighian corpuscles, is also incorrect. Malpighian corpuscles are found in the kidneys of mammals and birds, not in cockroaches. Option 4, Kidnev, is a misspelled word and not a valid option. Malpighian tubules, on the other hand, are long, slender tubes that remove waste materials from the body of a cockroach. They are located in the digestive system and help to remove nitrogenous waste from the hemolymph, the equivalent of blood in insects. These tubules play a crucial role in maintaining the osmotic balance of the cockroach`s body by removing metabolic waste products.