The total number of positive integral solutions (x, y, z) such that xyz = 24 is :

If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is $${{{x^2} - 4x + y + 8} \over {x - 2}}$$, then this curve also passes through the point :

Let f, g : N $$ \to $$ N such that f(n + 1) = f(n) + f(1) $$\forall $$ n$$\in$$N and g be any arbitrary function. Which of the following statements is NOT true?

Let the lines (2 $$-$$ i)z = (2 + i)$$\overline z $$ and (2 $$+$$ i)z + (i $$-$$ 2)$$\overline z $$ $$-$$ 4i = 0, (here i² = $$-$$1) be normal to a circle C. If the line iz + $$\overline z $$ + 1 + i = 0 is tangent to this circle C, then its radius is :