The Soviet leader who came to power after the death of Joseph Stalin was a man named Nikita Khrushchev.  Stalin died in 1953 and Khrushchev took power right after that.  He remained in power until he was thrown out of power in 1964.

Khrushchev was the leader of the Soviet Union through some of the most important events of the Cold War.  For example, he was the leader during the building of the Berlin Wall.  Perhaps more importantly, he was the Soviet leader who decided to put nuclear missiles in Cuba, leading to the Cuban Missile Crisis in 1962.  It was partly as a result of this that he lost power.

The choices are interesting, but the answer would have to be B) Nikita Khrushchev.  Khruschev was one of Stalin's closest advisers.  He also served as one of Stalin's generals during the Second World War.  Khruschev supported Stalinist purges and voiced much in way of support of his predecessor as he was a rising force in the Communist Party.  When Stalin died, Khruschev emerged as his successor and as leader of the Soviet Union.  As a leader, Khruschev distanced himself from the Stalinist purges and offered a more open, comparatively speaking, vision of the Soviet Union.  He still offered stiff and formidable opposition to the United States in the Cold War.  His role in this capacity was most notable in the Cuban Missile Crisis and the standoff with the United States, nuclear warheads hanging in the balance.  Khruschev was succeeded by Leonid Brezhnev.