The set of all $$\alpha $$ $$ \in $$ R, for which w = $${{1 + \left( {1 - 8\alpha } \right)z} \over {1 - z}}$$ is purely imaginary number, for all z $$ \in $$ C satisfying |z| = 1 and Re z $$ \ne $$ 1, is :

Let $$A$$ be a matrix such that $$A.\left[ {\matrix{ 1 & 2 \cr 0 & 3 \cr } } \right]$$ is a scalar matrix and |3A| = 108.
Then A² equals :

Let S be the set of all real values of k for which the systemof linear equations
x + y + z = 2
2x + y $$-$$ z = 3
3x + 2y + kz = 4
has a unique solution. Then S is :

If n is the degree of the polynomial,

$${\left[ {{2 \over {\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8} + $$ $${\left[ {{2 \over {\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8}$$

and m is the coefficient of xⁿ in it, then the ordered pair (n, m) is equal to :