Ajmer is a city in the north-western Indian state of Rajasthan. It serves as the administrative headquarters of the Ajmer district and Ajmer divisiā¦Ajmer is a city in the north-western Indian state of Rajasthan. It serves as the administrative headquarters of the Ajmer district and Ajmer division. It lies at the centre of Rajasthan, earning it the nickname 'the Heart of Rajasthan'.