In which year did China annex Tibet in the twentieth century?

1950

China annexed Tibet in 1950 and thus removed a historical buffer between India and China.

Two significant events strained the relationship between India and China. The annexation of Tibet by China in 1950 eliminated a historical buffer zone that had existed between the two nations.  In 1959, the Tibetan spiritual leader, the Dalai Lama, sought and received political asylum in India, causing China to accuse India of harboring anti-China activities.