The correct answer is: A. Ladakh
Gulab Singh was the Raja of Jammu from 1822 to 1857. He was a Dogra Rajput who came to power after the death of his father, Ranjit Dev. Gulab Singh was a skilled military leader and administrator, and he expanded the territory of Jammu Kingdom significantly. He conquered Ladakh in 1834, Kashmir in 1846, and the Chenab Valley in 1848.
Ladakh was not a part of Jammu Kingdom under Gulab Singh till 1846. It was ruled by the Ladakhi kings until it was conquered by Gulab Singh in 1834. After the conquest, Ladakh was merged with Jammu Kingdom and became a part of the Dogra Empire.
The other options, Kashmir, Rajouri, and Zanskar, were all a part of Jammu Kingdom under Gulab Singh. Kashmir was conquered by Gulab Singh in 1846, Rajouri was conquered in 1841, and Zanskar was conquered in 1840.