Let S = { $$x$$ $$ \in $$ R : $$x$$ $$ \ge $$ 0 and

$$2\left| {\sqrt x - 3} \right| + \sqrt x \left( {\sqrt x - 6} \right) + 6 = 0$$}. Then S

If f(x) is a quadratic expression such that f (1) + f (2) = 0, and $$-$$ 1 is a root of f (x) = 0, then the other root of f(x) = 0 is :

If tanA and tanB are the roots of the quadratic equation, 3x² $$-$$ 10x $$-$$ 25 = 0, then the value of 3 sin²(A + B) $$-$$ 10 sin(A + B).cos(A + B) $$-$$ 25 cos²(A + B) 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 :