According to Genesis 8:5, the mountain tops first became visible in the tenth month after the Flood began. The verse says that, as the waters continued to decrease, the tops of the mountains appeared.
This detail belongs to a sequence of dates in the Flood narrative. Genesis says the ark came to rest in the seventh month, while the mountain tops became visible in the tenth month. The text therefore distinguishes the ark’s resting from the later visibility of high ground.
After waiting further, Noah sends a raven and then doves to test whether the land has dried. Eventually, in the six hundred and first year of Noah’s life, the covering of the ark is removed and the ground is described as dry.
Readers sometimes confuse the seventh month with the tenth month. The seventh month marks the ark’s resting on the mountains of Ararat; the tenth month marks the appearance of the mountain tops. The requested answer is the tenth month.