Nitrogenous wastes

Ammonotelic animals excrete ammonia, which is highly toxic and needs a large amount of water for its removal: many bony fishes, aquatic amphibians and aquatic insects.
Ureotelic animals excrete urea: mammals (humans), many terrestrial amphibians (adult frog) and marine fishes.
Uricotelic animals excrete uric acid as a pellet or paste with minimum loss of water: reptiles (lizards), birds (pigeon), land snails and insects (cockroach).
Checking the six animals: aquatic amphibia are ammonotelic; frog and humans are ureotelic; pigeon, lizards and cockroach are uricotelic.
Hence the correct categorisation is Ammonotelic – aquatic amphibia; Ureotelic – frog, humans; Uricotelic – pigeon, lizards, cockroach.

Uricotelic animals excrete nitrogenous wastes as uric acid, in the form of a pellet or paste, with a minimum loss of water.
Reptiles, birds, land snails and insects are uricotelic.
Amphibians are ureotelic when terrestrial (adult frog) and ammonotelic when aquatic.
Annelids (earthworms) are mainly ureotelic or ammonotelic, depending on the availability of water.
The only pair in which both groups are uricotelic is reptiles and birds.

Humans are ureotelic; the principal nitrogenous waste is urea.
Ammonia produced by the metabolism of amino acids is converted into urea in the liver through the ornithine (urea) cycle.
Urea is released into the blood, filtered out by the kidneys and excreted in the urine.
Only small amounts leave the body by other routes such as sweat.
Hence it is synthesised in the liver but eliminated mostly through the kidneys.

Uricotelic animals excrete nitrogenous waste as uric acid, in the form of a pellet or paste, with minimum loss of water. Reptiles, birds, land snails and insects are uricotelic.
The cockroach is an insect; its Malpighian tubules remove nitrogenous wastes, which are excreted as uric acid.
The adult frog and man are ureotelic (urea is the main waste).
The earthworm is mainly ureotelic or ammonotelic, depending on the availability of water.
Hence uric acid is the chief nitrogenous waste of the cockroach.