The correct answer is (a). Garhwal was under Gorkha rule from 1804 to 1815. The Gorkhas were a Nepalese people who invaded Garhwal in 1804. They defeated the Garhwal rulers and took control of the region. The Gorkhas ruled Garhwal for 11 years, until they were defeated by the British in the Anglo-Gorkha War of 1814-1816. After the war, Garhwal was returned to its former rulers.
Option (b) is incorrect because the Gorkhas ruled Garhwal for 11 years, not 22 years. Option (c) is incorrect because the Gorkhas ruled Garhwal from 1804 to 1815, not from 1800 to 1835. Option (d) is incorrect because the Gorkhas ruled Garhwal for 11 years, not 97 years.