A is binary compound of a univalent metal. 1.422 g of A reacts completely with 0.321 g of sulphur in an evacuated and sealed tube to give 1.743 g of a white crystalline solid B, that forms a hydrated double salt, C with Al₂ (SO₄)₃ . Identify A, B and C.

The circle $${x^2} + {y^2} = 1$$ cuts the $$x$$-axis at $$P$$ and $$Q$$. Another circle with centre at $$Q$$ and variable radius intersects the first circle at $$R$$ above the $$x$$-axis and the line segment $$PQ$$ at $$S$$. Find the maximum area of the triangle $$QSR$$.

Find the indefinite integral $$\,\int {\cos 2\theta {\mkern 1mu} ln\left( {{{\cos \theta + \sin \theta } \over {\cos \theta - \sin \theta }}} \right)} {\mkern 1mu} d\theta $$

The value of $$\int\limits_2^3 {{{\sqrt x } \over {\sqrt {3 - x} + \sqrt x }}} dx$$ is ...........