Explanation:

- Vembanad Lake is the longest lake in India, with a significant ecological and cultural importance in the country.

- It is also the largest lake in the Indian state of Kerala. Kerala is located in the southwestern part of India and is known for its picturesque backwaters and rich biodiversity.

- Sikkim is a northeastern state known mainly for its mountainous terrain and is not associated with large lakes like Vembanad.

- Odisha is located on the eastern coast of India, home to several large and famous lagoons like Chilika Lake, but not Vembanad.

- Assam is in northeastern India, known for its river systems, especially the Brahmaputra, but not for Vembanad Lake.

- Gujarat is a western state with the Great Rann of Kutch, but it does not contain Vembanad Lake.