Hint:Shankar Aacharya or Shankar was born during the period of bhakti tradition in the 8th century. He was born in a place which was a few kilometres away from Aluva in Ernakulam district. His birthplace is famous for many important temples and shrines dedicated to Saradha Devi, Shri Shankara, Shri Krishna and etc.
Complete answer: Shankara was one of the most influential philosophers of India belonging to the period of bhakti tradition. He was born in Kalady, Kerala in the 8th century. He was an advocate of Advaita and the doctrine based on the supreme God and oneness of the individual soul which is the ultimate reality. His teachings included that Brahmins who were regarded as only or ultimate reality were formless and without any attributes.
-Ramanuja was born in Sriperumbudur in Tamil Nadu in the 11th century. He was influenced by the Alvars and propounded the doctrine of Vishishtadvaita. He believed that salvation can be attained through intense devotion to Vishnu.
-There are many influential philosophers who are born in Karnataka like Basavanna, Allama Prabhu etc but not exactly in the Kelady town. Same is the case of Andhra Pradesh.
Therefore the correct answer is option-A.
Note: According to Shankaracharya, the world around us is an illusion or Maya and preached renunciation of the world and adoption of the path of knowledge to understand the true nature of brahmins and their philosophies and finally to attain salvation.