The correct answer is option 1: The Nanda dynasty. During Alexander`s invasion of India in the 4th century BCE, the Nanda dynasty was in power. The Nanda dynasty ruled over the Magadha region of ancient India from approximately 343 BCE to 322 BCE. This dynasty was founded by Mahapadma Nanda and was known for its wealth and military power.

Option 2, the Maurya dynasty, is incorrect as it succeeded the Nanda dynasty. The Maurya dynasty, founded by Chandragupta Maurya, rose to power after overthrowing the Nanda dynasty.

Option 3, the Sunga dynasty, is incorrect as it ruled India after the Maurya dynasty. The Sunga dynasty replaced the Maurya dynasty in around 185 BCE.

Option 4, the Kanva dynasty, is incorrect as it also ruled after the Maurya dynasty. The Kanva dynasty came into power around 75 BCE, succeeding the Sunga dynasty.

Therefore, the correct answer is option 1, the Nanda dynasty, which was ruling at the time of Alexander`s invasion.