Let $$f$$ be a differentiable function such that $${x^2}f(x) - x = 4\int\limits_0^x {tf(t)dt} $$, $$f(1) = {2 \over 3}$$. Then $$18f(3)$$ is equal to :

Let the first term $$\alpha$$ and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to

Let the complex number $$z = x + iy$$ be such that $${{2z - 3i} \over {2z + i}}$$ is purely imaginary. If $${x} + {y^2} = 0$$, then $${y^4} + {y^2} - y$$ is equal to :

Let $$f:( - 2,2) \to R$$ be defined by $$f(x) = \left\{ {\matrix{ {x[x],} & { - 2 < x < 0} \cr {(x - 1)[x],} & {0 \le x \le 2} \cr } } \right.$$ where $$[x]$$ denotes the greatest integer function. If m and n respectively are the number of points in $$( - 2,2)$$ at which $$y = |f(x)|$$ is not continuous and not differentiable, then $$m + n$$ is equal to ____________.