A cell, Ag | Ag⁺ || Cu²⁺ | Cu, initially contains 1 M Ag⁺ and 1 M Cu²⁺ ions. Calculate the change in the cell potential after the passage of 9.65 A current for 1 h.

The rate constant for an isomerisation reaction, A $$\to$$ B is 4.5 $$\times$$ 10^-3 min^-1. If the initial concentration of A is 1 M, calculate the rate of the reaction after 1 h.

Let $$f(x)$$ be a continuous function given by $$$f\left( x \right) = \left\{ {\matrix{ {2x,} & {\left| x \right| \le 1} \cr {{x^2} + ax + b,} & {\left| x \right| > 1} \cr } } \right\}$$$

Find the area of the region in the third quadrant bounded by the curves $$x = - 2{y^2}$$ and $$y=f(x)$$ lying on the left of the line $$8x+1=0.$$

Integrate $$\int\limits_0^\pi {{{{e^{\cos x}}} \over {{e^{\cos x}} + {e^{ - \cos x}}}}\,dx.} $$