Let f be a bounded, twice continuously differentiable real-valued function on (0, ∞) such that f(x) > 0 for all x ∈ (0, ∞). Which of the following statements is necessarily true?

Which of the following territories was annexed by Lord Dalhousie under the pretext of misgovernance, and not directly through the Doctrine of Lapse?

What was the primary stated reason for the Partition of Bengal in 1905 by Lord Curzon?