Step 1: Understanding the Concept:
The British East India Company used several different methods to annex Indian territories in the mid-19th century.
Step 2: Detailed Explanation:
The map points to Awadh (Oudh).
Lord Dalhousie annexed Awadh in 1856. Unlike states like Satara or Jhansi, which were annexed under the Doctrine of Lapse because they had no natural heir, Awadh had many heirs.
The British justified the annexation of Awadh by claiming that the Nawab, Wajid Ali Shah, was incapable of ruling and that there was widespread "misgovernance."
Step 3: Final Answer:
Awadh was annexed on the pretext of misgovernance.
Hence, the correct option is (C).