The correct option is D Fear of resistance from Sikh soldiers.
The British did not annex Punjab after the First Anglo-Sikh War because they had already defeated the Sikhs at the battles of Mudki, Ferozeshah, and Sabhraon. But they feared resistance from Sikh soldiers camping at Lahore, Amritsar, and Peshawar. Lord Hardinge calculated the expenditure of maintaining law and order in Punjab, and it outweighed their income. Punjab was a buffer zone between the forces of the British Empire and Afghanistan.