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 ____________.
Let $$y = p(x)$$ be the parabola passing through the points $$( - 1,0),(0,1)$$ and $$(1,0)$$. If the area of the region $$\{ (x,y):{(x + 1)^2} + {(y - 1)^2} \le 1,y \le p(x)\} $$ is A, then $$12(\pi - 4A)$$ is equal to ___________.
The number of elements in the set $$\{ n \in Z:|{n^2} - 10n + 19| < 6\} $$ is _________.
If the mean of the frequency distribution
Class : | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
---|---|---|---|---|---|
Frequency : | 2 | 3 | $$x$$ | 5 | 4 |
is 28, then its variance is __________.