Yes, the year 1924 is considered to be in the 20th century. The 20th century began on January 1, 1901, and ended on December 31, 2000. To determine if a specific year falls within the 20th century, you need to check if it is between these two dates. In the case of 1924, it falls within that time range, so it is indeed part of the 20th century.
