The Mauryan Empire extended its control over Goa during the reign of:

Ashoka the Great
Chandragupta Maurya
Bindusara
Samudragupta

The correct answer is: Ashoka the Great.

Ashoka the Great was the third emperor of the Mauryan Empire, reigning from 272 to 232 BCE. He was the grandson of Chandragupta Maurya, the founder of the Mauryan Empire. Ashoka is best known for his military conquests, which extended the Mauryan Empire to its greatest extent. However, he is also known for his Buddhist reforms and his promotion of non-violence.

Goa was one of the many territories that Ashoka conquered during his reign. He annexed the region in 265 BCE, after defeating the Satavahana dynasty. Ashoka’s conquest of Goa marked the beginning of the Mauryan Empire’s rule over the region. The Mauryans ruled Goa for over a century, until the empire collapsed in 185 BCE.

The other options are incorrect. Chandragupta Maurya was the founder of the Mauryan Empire, but he did not extend its control over Goa. Bindusara was the second emperor of the Mauryan Empire, and he did not extend its control over Goa either. Samudragupta was the grandson of Ashoka the Great, and he ruled the Mauryan Empire from 335 to 375 CE. He did not extend the empire’s control over Goa, but he did conquer many other territories in India.