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 :

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 :

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 :

If $$\lambda $$ $$ \in $$ R is such that the sum of the cubes of the roots of the equation,
x² + (2 $$-$$ $$\lambda $$) x + (10 $$-$$ $$\lambda $$) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :