The charter of the united nations was adopted a) immediately following the last session of the league of nations b) in the year after world war 11 ended c) after the cold war began d) at the beginning of world war 11

The best choice among those options would likely be "after the Cold War began."  The tensions between the United States along with the other western members of the Allies, over against the Soviet Union, began already as soon as Germany was defeated in World War II.  Following Germany's surrender in May, 1945, the tensions between the USA and the USSR would begin to evidence themselves.

The charter of the United Nations was signed/adopted on June 26, 1945 and went into effect October 24, 1945.

The last session of the League of Nations was held in April, 1946, and its functions were taken over by the United Nations.