The correct answer is (a) Joseph Hooker.
Joseph Dalton Hooker (1817-1911) was a British botanist and explorer. He was a friend and colleague of Charles Darwin, and he accompanied Darwin on his voyage on the HMS Beagle. Hooker is best known for his work on the flora of the Himalayas, and he is credited with discovering the Valley of Flowers in 1841.
William Moorcroft (1767-1825) was an English explorer and physician. He was the first European to travel to Ladakh and Tibet, and he made significant contributions to the knowledge of the geography and natural history of these regions. However, he is not credited with discovering the Valley of Flowers.
Frank Smythe (1883-1949) was a British mountaineer. He was the first person to climb Kamet, the second-highest mountain in the Garhwal Himalayas. However, he is not credited with discovering the Valley of Flowers.
Nain Singh Rawat (1824-1893) was an Indian explorer. He was employed by the British Survey of India, and he made several important journeys to Tibet. However, he is not credited with discovering the Valley of Flowers.