The correct answer is option 2, Corbett. Corbett National Park, located in the Nainital district of Uttarakhand, was established in 1936. It was the first national park to be established in India and is named after Jim Corbett, a British conservationist and author. The main aim of establishing Corbett National Park was to protect the endangered Bengal tiger. The park is known for its diverse flora and fauna and is home to various species of animals, including tigers, elephants, leopards, and deer.

Option 1, Bandipur, is incorrect. Bandipur National Park is located in Karnataka and was established in 1974.

Option 3, Velavadar, is also incorrect. Velavadar National Park, now known as Blackbuck National Park, is located in Gujarat and was established in 1976.

Option 4, Periyar, is incorrect as well. Periyar National Park, also known as Periyar Tiger Reserve, is located in Kerala and was established in 1978.

Therefore, the correct answer is option 2, Corbett, as it was the first national park established in India in 1936.