The following electrochemical cell has been set up.
Pt(1) | Fe³⁺, Fe²⁺ (a = 1) | Ce⁴⁺, Ce³⁺ (a=1) | Pt(2)
E^o (Fe³⁺, Fe²⁺) = 0.77 V; E^o (Ce⁴⁺, Ce³⁺) = 1.61 V
If an ammeter is connected between the two platinum electrodes, predict the direction of flow of current. Will the current increase or decrease with time?

A hydrogenation reaction is carried out at 500 K. If the same reaction is carried out in the presence of a catalyst at the same rate, the temperature required is 400 K. Calculate the activation energy of the reaction if the catalyst lowers the activation barrier by 20 kJ mol^-1.

In any triangle $$ABC,$$ prove that $$$\cot {A \over 2} + \cot {B \over 2} + \cot {C \over 2} = \cot {A \over 2}\cot {B \over 2}\cot {C \over 2}.$$$

If $$\alpha ,\,\beta $$ are the roots of $$a{x^2} + bx + c = 0$$, $$\,\left( {a \ne 0} \right)$$ and $$\alpha + \delta ,\,\,\beta + \delta $$ are the roots of $$A{x^2} + Bx + c = 0,$$ $$\left( {A \ne 0\,} \right)\,$$ for some contant $$\delta $$, then prove that $${{{b^2} - 4ac} \over {{a^2}}} = {{{B^2} - 4Ac} \over {{A^2}}}$$.