In the reaction


The product $$E$$ is :

Match the catalysts to the correct processes :

	Catalyst		Process
(A)	TiCl3	(i)	Wacker process
(B)	PdCl2	(ii)	Ziegler - Natta polymerization
(C)	CuCl2	(iii)	Contact process
(D)	V2O5	(iv)	Deacon's process

A complex number z is said to be unimodular if $$\,\left| z \right| = 1$$. Suppose $${z_1}$$ and $${z_2}$$ are complex numbers such that $${{{z_1} - 2{z_2}} \over {2 - {z_1}\overline {{z_2}} }}$$ is unimodular and $${z_2}$$ is not unimodular. Then the point $${z_1}$$ lies on a :

Let $$\alpha $$ and $$\beta $$ be the roots of equation $${x^2} - 6x - 2 = 0$$. If $${a_n} = {\alpha ^n} - {\beta ^n},$$ for $$n \ge 1,$$ then the value of $${{{a_{10}} - 2{a_8}} \over {2{a_9}}}$$ is equal to :