Did the twentieth century span the years 1900–1999 or the years 1901–2000?
According to the style manual, centuries should be spelled out in lower case. Therefore the correct spelling of "twentieth century" should be lower not upper case like "Twentieth Century". The style manual also indicates that beginning and ending years should be separated with an en-dash as in 1900-1999 or 1901-2000.
The only answer choice that does both of these correctly is the second one.