The Edison storage cells is represented as
Fe(s) | FeO(s) | KOH (aq) | Ni₂O₃(s) | Ni(s)
The half-cell reactions are:
Ni₂O₃ + H₂O (l) + 2e^- $$\leftrightharpoons$$ 2NiO(s) + 2OH^-; E^o = +0.40V
FeO(s) + H₂O(l) + 2e^- $$\leftrightharpoons$$ Fe(s) + 2OH^-; E^o = -0.87V
(i) What is the cell reaction?
(ii) What is the cell e.m.f? How does it depend on the concentration of KOH?
(iii) What is the maximum amount of electrical energy that can be obtained from one mole of Ni₂O₃?

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