For the given reactions, A + B $$\to$$ Products, following data were obtained
(a) Write the rate law expression
(b) Find the rate constant

Find the centre and radius of circle given by $$\,\left| {{{z - \alpha } \over {z - \beta }}} \right| = k,k \ne 1\,$$

where, $${\rm{z = x + iy, }}\alpha {\rm{ = }}\,{\alpha _1}{\rm{ + i}}{\alpha _2}{\rm{,}}\,\beta = {\beta _1}{\rm{ + i}}{\beta _2}{\rm{ }}$$

If $$a,\,b,c$$ are positive real numbers. Then prove that $$${\left( {a + 1} \right)^7}{\left( {b + 1} \right)^7}{\left( {c + 1} \right)^7} > {7^7}\,{a^4}{b^4}{c^4}$$$

Prove by permulation or otherwise $${{({n^2})!} \over {{{(n!)}^n}}}$$ is an integer $$(n \in {1^ + })$$.