Step 1: Understanding the Concept:
This question asks about the year of Mikhail Gorbachev's resignation, a pivotal event that marked the end of an era. It is important to note a factual inaccuracy in the question: Mikhail Gorbachev was the President of the Soviet Union (USSR), not Russia. The first President of Russia was Boris Yeltsin.
Step 2: Detailed Explanation:
After a failed coup against him in August 1991, Gorbachev's power significantly weakened, while the power of the individual Soviet republics and their leaders, especially Russia's Boris Yeltsin, grew stronger.
One by one, the republics declared their independence from the Soviet Union.
Recognizing that the Soviet Union had effectively ceased to exist, Mikhail Gorbachev resigned from his post as the President of the Soviet Union on December 25, 1991.
The following day, December 26, 1991, the Soviet Union was formally dissolved.
Step 3: Final Answer:
Mikhail Gorbachev resigned as the President of the Soviet Union in the year 1991.
Therefore, option (B) is the correct answer.