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The Doctrine of Lapse was a policy introduced by the British East India Company in the 19th century. According to this doctrine, if a ruler of a Princely State died without a natural heir, the state would be annexed by the British Empire. This policy was used to expand British control over the Indian subcontinent.
In the case of the question, the Doctrine of Lapse was first applied to the Princely State of Satara. Satara was a Maratha kingdom located in present-day Maharashtra, India. When the last ruler of Satara, Shahaji II, died without a natural heir in 1848, the British used the Doctrine of Lapse to annex the state and bring it under British control.
It is important to note that while the answer provided is generally correct, it is always recommended to cross-check the information for accuracy.