The Nanda dynasty of Magadha was established by:

The Nanda dynasty of Magadha was founded by Mahapadma Nanda in the 4th century BCE (around 345 BCE, according to many scholars).

About Mahapadma Nanda:

• According to the Puranas, he was the son of the last Shishunaga king by a Shudra woman; according to Jain and Greek accounts, he was the son of a barber.
• He is described in the Puranas as "Sarva-kshatrantaka" ("destroyer of all Kshatriyas") and "Ekarat" ("sole sovereign"), because he defeated many Kshatriya ruling families.
• He is also called "Ugrasena" in Buddhist texts.
• He is sometimes described as the first "empire-builder" of Indian history, as he brought a large part of northern India under one rule.
• His empire may have included Kalinga.

Features of the Nanda empire:

• The Nandas were very wealthy; their wealth and large army are mentioned by Greek writers.
• According to Greek accounts, at the time of Alexander's invasion, the Nanda army had about 2,00,000 infantry, 20,000 cavalry, 2,000 chariots and 3,000-4,000 elephants.
• The fear of this army is said to be one of the reasons why Alexander's soldiers refused to march further east beyond the Beas river.
• They developed a system of taxation and administration.
• The Nandas were unpopular because of their heavy taxes, according to some sources.

Dynasties of Magadha:

• Haryanka dynasty (founded by Bimbisara, according to some sources).
• Shishunaga dynasty (founded by Shishunaga; he conquered Avanti).
• Nanda dynasty (founded by Mahapadma Nanda).
• Maurya dynasty (founded by Chandragupta Maurya).

Why not the other options?

• ✗Ugrasena is another name of Mahapadma Nanda in some texts, but it is not the usual answer.
• ✗Shishunaga founded the Shishunaga dynasty.
• ✗Kalashoka was a Shishunaga ruler.