In which year was a separate Andhra state formed after the linguistic reorganisation of the then Madras province?

1953

The correct answer is Option 2- 1953

A separate Andhra state was formed after the linguistic reorganisation of the Madras province in 1953.

For clarity:
Andhra State: Carved out of the Telugu-speaking northern districts of Madras State on October 1, 1953.
Andhra Pradesh: Formed in 1956 by merging the Telugu-speaking regions of Hyderabad State with the existing Andhra State.
Therefore, while Andhra Pradesh as a state encompassing the entire Telugu region came into existence in 1956, the initial separate state based solely on Telugu speaking areas emerged in 1953.