The correct options are
A To expand the British rule.
B To acquire more territories.
The Doctrine of Lapse was a political weapon used by Lord Dalhousie to expand the British Empire in India by acquiring more territories. The Hindu law permitted Hindu kings to adopt their successors, but, according to Dalhousie's doctrine, they had to seek the permission of the Company to do so. The Company refused, and without a natural heir, their kingdoms automatically integrated into the British Empire.