Let V be the vector space of all real-valued continuous functions on [0, π]. By defining the inner product as ⟨f, g⟩ = ∫0π f(x)g(x) dx, find the value of ⟨x, sin x⟩.

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?