The correct answer is option 'A', the Yellow Turban Rebellion took place during the Han dynasty. Let's delve into the details of this rebellion and its historical context.

The Han dynasty was one of the most crucial periods in Chinese history, spanning over four centuries from 206 BCE to 220 CE. During this time, China experienced significant political, economic, and social transformations.

The Yellow Turban Rebellion was a massive uprising that occurred during the late Eastern Han dynasty, specifically between 184 and 205 CE. This rebellion was led by a Taoist sect known as the Way of Peace, whose members wore yellow turbans as a symbol of their movement. The rebellion was named after this distinctive feature.

Below, we will explore the key aspects of the Yellow Turban Rebellion:

1. Causes of the Rebellion:
- Agrarian Crisis: The Han dynasty faced various challenges, including a severe agrarian crisis. This crisis resulted from a combination of factors such as floods, droughts, and ineffective governance, leading to widespread poverty and food shortages.
- Corruption and Inequity: The central government was plagued by corruption and inefficiency, with high-ranking officials exploiting their positions for personal gain. This exacerbated the grievances of the common people, who were burdened by heavy taxes and unequal treatment.

2. Objectives of the Rebellion:
- End of the Han dynasty: The rebellion aimed to overthrow the Han dynasty and establish a new order that would rectify the perceived injustices and bring about a more equitable society.
- Reducing social inequality: The Yellow Turbans advocated for land redistribution and the abolition of oppressive taxes, seeking to alleviate the suffering of the peasant class.

3. Rebellion's Impact:
- Geographic Spread: The rebellion quickly spread across a vast territory, with various factions rising up in different regions of China.
- Government Response: Initially caught off guard, the Han government struggled to suppress the rebellion. However, they eventually mobilized their forces and launched counteroffensives.
- Collapse of the Han Dynasty: While the rebellion was eventually quelled, it contributed to the weakening of the Han dynasty. The rebellion exposed the government's vulnerabilities and marked the beginning of a period of political fragmentation and instability in China.

In conclusion, the Yellow Turban Rebellion was a significant event that occurred during the Han dynasty. It emerged as a response to the agrarian crisis, corruption, and social inequality prevalent during that time. The rebellion aimed to bring about a new order and address the grievances of the common people. While the rebellion was ultimately suppressed, its impact on the Han dynasty and Chinese history cannot be overlooked.