What were the causes of decline in central authority in China in the 19th and early 20th century

This section focuses on four key topics in China's modern history. The first is that of China's conflict with an aggressively expanding West in the 1800s, beginning with the demands made by England at the end of the eighteenth century; England, as was true with the other imperial powers, was intent on "opening up" trade with China. Chinese denials for trade on England's terms eventually led to several wars which concluded by imposing "unequal" treaties that by the end of the century threatened to carve up China "like a melon."

A second key topic is that of the internal crises that were occurring in China at this time: the rebellions, famines, and explosive population growth of the eighteenth and nineteenth centuries. Many of these issues were not new to the empire, but the extent and the timing of their challenge was crucial, coming at the same time as foreign encroachments.

A third major topic is that of the dialogue within China about how best to respond to these combined challenges and the extent and nature of the changes that were required. Dialogue about reform was many-faceted, and it vacillated between the progressive combination of elements from the West with the best of Chinese traditions, to the outright rejection of the Chinese past. Finally, by the 1920s, some reformers turned revolutionary, discussing the relevance of Marxism for China.

The fourth major topic is that of the Chinese communist revolution that unfolded in China in the 1930s and 1940s and the particular role played by Mao Zedong (Mao Tse-tung) in adapting Marxism to the Chinese situation.

China in the 19th and Early 20th Centuries

China in the 1800s

In the 16th century, the Chinese economy was still the most sophisticated and productive in the world, and the Chinese probably enjoyed a higher standard of living than any other people on earth. The Qing (Ch'ing) Dynasty (1644-1912), founded by the invading Manchus, continued this splendor. Contemporary Chinese called the 18th century "unparalleled in history," when all aspects of culture flourished. China was a prosperous state with abundant natural resources, a huge but basically contented population, and a royal house of great prestige at home and abroad.

Explanation: hope this helps :)

nations must cooperate to bring about and maintain world peace.

nations must not wage wars or commit war crimes in a desire to control other nations.

i think i know which options you have but if these aren't options let me know