The correct answer is option 4, Punjab. The "Doctrine of Lapse" was a policy followed by the British East India Company during the 19th century, which allowed them to annex Indian states if they had no male heir to succeed the throne. However, in the case of Punjab, this policy was not followed. Instead, the British entered into a series of wars with the Sikh Empire in Punjab, known as the Anglo-Sikh Wars, and eventually defeated them. After their victory, Punjab was not annexed using the Doctrine of Lapse, but instead, a treaty was signed called the Treaty of Lahore which allowed the British to have control and influence over the region. So it can be said that the Doctrine of Lapse was not applied to the annexation of Punjab.