Which state's residents are called "Buckeyes"?

Which state is known as "The Land of Enchantment"? Which state is known as "The Mount Rushmore State"? Which state is known as "The Peace Garden State"? Which state's residents are called "Hoosiers"? Which state's residents are called "Sooners"? Which state is the largest by area? Which state is the smallest by area? Which state has the largest population?