Explanation:

- Telangana shares its capital city with Option 1: Andhra Pradesh.

- Hyderabad is the shared capital of both Telangana and Andhra Pradesh, as per the Andhra Pradesh Reorganisation Act, 2014. However, this arrangement was set to be temporary, up to 10 years from the formation of Telangana in 2014.

- Option 2: Karnataka

- Bengaluru is the capital of Karnataka. It doesn't serve as a capital for any other state.

- Option 3: Odisha

- Bhubaneswar is the capital of Odisha. Odisha does not share its capital with any other state.

- Option 4: Kerala

- Thiruvananthapuram is Kerala’s capital, and it is unique to the state.

So the correct answer is definitely Option 1: Andhra Pradesh.