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1.
Unconquerable/unbeatable/invincible. The name is of Indo-Aryan origin and literally means "the one who cannot be defeated". "Jit" literally means victory and the "A" individualizes it. It can also mean unconquerable, unbeatable, invincible, etc.
That man's name is Ajit which means unconquerable.
by Benn_Blanco March 13, 2010
 
2.
Ajit is a popular Punjabi/Sikh name given which originated from the son of Sri Guru Gobind Singh Ji, the 10th Sikh guru's eldest son, Sahibzada Ajit Singh. Below is a profile biography of Sahibzada Ajit Singh.

Sahibzada Ajit Singh (1687 - 1705), was the eldest of Guru Gobind Singh's four sons. His younger brothers were Sahibzada Jujhar Singh, Sahibzada Zorawar Singh and Sahibzada Fateh Singh. With his three brothers, Sahibzada Ajit Singh carried on a great family tradition: that of attaining the status of one of the most hallowed martyrs in Sikh history. Before him and his brothers, their grandfather, the ninth Sikh Guru, Guru Tegh Bahadur and great-great grandfather, the fifth Sikh Guru, Guru Arjan Dev had also been executed by the Mughals (Muslim extremist warriors).
Ajit is a business man who works in that building over there. He is highly successful and earns an honest living.
by Cytrus June 29, 2006