The correct answer is option 'D) Gupta Dynasty'. Let's understand why the Gupta Dynasty arose in Magadha in the fourth century A.D.

The Gupta Dynasty was one of the most influential dynasties in ancient India, ruling from approximately the fourth to the sixth century A.D. It emerged in the region of Magadha, located in present-day Bihar and eastern Uttar Pradesh. The rise of the Gupta Dynasty marked a significant period in Indian history, known as the Golden Age of India.

The Gupta Dynasty was established by Chandragupta I, who married into a powerful family and inherited their kingdom in Magadha. Chandragupta I laid the foundation for the dynasty's rise to power, but it was his son, Samudragupta, who expanded and consolidated the empire.

Here are some key points about the Gupta Dynasty:

1. Chandragupta I:
- Chandragupta I was the founder of the Gupta Dynasty.
- He married Kumaradevi, the Lichchhavi princess, which helped him gain influence and power.
- Chandragupta I ruled from approximately 320 to 335 A.D.

2. Samudragupta:
- Samudragupta was the son of Chandragupta I and is considered one of the greatest rulers of the Gupta Dynasty.
- He expanded the empire through military conquests, establishing control over various regions of northern and central India.
- Samudragupta's empire extended from Bengal in the east to Gujarat in the west and from the Himalayas in the north to the Narmada River in the south.

3. Chandragupta II (Chandragupta Vikramaditya):
- Chandragupta II, also known as Chandragupta Vikramaditya, was another important ruler of the Gupta Dynasty.
- He further expanded the empire and strengthened its cultural and economic influence.
- Chandragupta II's reign is often considered the pinnacle of the Gupta Dynasty's power and prosperity.

4. Achievements and Contributions:
- The Gupta Dynasty is known for its significant contributions in various fields, including art, literature, science, and mathematics.
- It witnessed a flourishing of Indian art and literature, with notable advancements in architecture, sculpture, and poetry.
- The Gupta period is often referred to as the "Golden Age of India" due to the remarkable progress in intellectual and cultural pursuits.

In conclusion, the Gupta Dynasty arose in Magadha in the fourth century A.D. under the leadership of Chandragupta I. Through strategic marriages and military conquests, the dynasty expanded its influence and established a prosperous empire that left a lasting impact on Indian history and culture.