The correct answer is (a). Tamil is the official language of Tamil Nadu. It is the oldest language in the world still in use, and is spoken by over 70 million people worldwide. Tamil is a Dravidian language, and is not related to the Indo-Aryan languages such as Hindi and English.
Option (b) is incorrect because English is not an official language of Tamil Nadu. English is a widely spoken language in Tamil Nadu, but it is not an official language.
Option (c) is incorrect because Hindi is not an official language of Tamil Nadu. Hindi is an official language of India, but it is not an official language of Tamil Nadu.
Option (d) is incorrect because English is not the only official language of Tamil Nadu. Tamil is the only official language of Tamil Nadu.