The correct answer is: a) Linguistic lines.
The formation of Madras State in 1953 was based primarily on linguistic lines. The state was formed by merging the Madras Presidency, the Telugu-speaking areas of the erstwhile Hyderabad State, and the Kannada-speaking areas of the erstwhile Mysore State. The formation of Madras State was a major step in the process of linguistic reorganization of states in India.
The other options are incorrect. Option b) is incorrect because the formation of Madras State was not based on historical kingdoms. The Madras Presidency was a British colonial entity, and the Telugu-speaking areas of the erstwhile Hyderabad State and the Kannada-speaking areas of the erstwhile Mysore State were also under British rule. Option c) is incorrect because the formation of Madras State was not based on administrative convenience. The Madras Presidency was already a large and complex administrative unit, and the merger of the Telugu-speaking areas and the Kannada-speaking areas only made it more complex. Option d) is incorrect because the formation of Madras State was not based on economic considerations. The Madras Presidency was already a prosperous region, and the merger of the Telugu-speaking areas and the Kannada-speaking areas did not significantly alter its economic profile.