According to the common tradition of Vaishnavism, how many main incarnations (avatars) of Vishnu are recognised (the 'Dashavatara')?

According to the common tradition of Vaishnavism, ten main incarnations (avatars) of Vishnu are recognised, together called the "Dashavatara" (ten avatars).

The ten avatars (in the common list):

• Matsya: the fish, who saved Manu and the Vedas from the great flood.
• Kurma: the tortoise, who supported the mountain Mandara during the churning of the ocean.
• Varaha: the boar, who rescued the earth (Bhudevi) from the ocean.
• Narasimha: the man-lion, who killed the demon Hiranyakashipu to protect his devotee Prahlada.
• Vamana: the dwarf, who took the universe in three steps from the demon king Bali.
• Parashurama: the warrior-sage with an axe.
• Rama: the hero of the Ramayana.
• Krishna: the hero of the Mahabharata and the Bhagavata Purana (in some lists, Balarama is included, and Krishna is regarded as the source of all avatars).
• Buddha: included in many lists from the early medieval period (in some lists, replaced by Balarama).
• Kalki: the future avatar, who will appear at the end of the Kali Yuga to destroy evil.

The idea of avatars:

The concept is explained in the Bhagavad Gita: whenever righteousness (dharma) declines and unrighteousness increases, God takes a form on earth to protect the good and destroy the wicked.

Larger lists:

The Bhagavata Purana mentions 22 or 24 avatars, including sages and others.

In art and literature:

• The Dashavatara is a common theme in temple sculpture, painting and literature.
• The 12th-century poet Jayadeva's "Gita Govinda" begins with a hymn praising the ten avatars.
• The Dashavatara temple at Deogarh (Uttar Pradesh), built in the Gupta period, is one of the earliest stone temples in north India.
• The Varaha cave at Udayagiri (Madhya Pradesh) has a famous Gupta-period image of Varaha.
• "Dashavatara" is also a form of folk theatre in Goa and the Konkan region.

Vaishnavism:

• It is the tradition of Hinduism in which Vishnu (or his avatars, especially Krishna and Rama) is worshipped as the supreme God.
• In the Bhakti movement, the Alvars of Tamil Nadu and later saints spread Vaishnava devotion.

Why not the other options?

• ✗7, 12 and 24 are not the standard number; 24 is mentioned in some longer lists.