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 :

If x₁, x₂, . . ., x_n and $${1 \over {{h_1}}}$$, $${1 \over {{h_2}}}$$, . . . , $${1 \over {{h_n}}}$$ are two A.P..s such that x₃ = h₂ = 8 and x₈ = h₇ = 20, then x₅.h₁₀ equals :

If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

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 :