Let $$f(x)=\left\{\begin{array}{l}\left|4 x^{2}-8 x+5\right|, \text { if } 8 x^{2}-6 x+1 \geqslant 0 \\ {\left[4 x^{2}-8 x+5\right], \text { if } 8 x^{2}-6 x+1<0,}\end{array}\right.$$ where $$[\alpha]$$ denotes the greatest integer less than or equal to $$\alpha$$. Then the number of points in $$\mathbf{R}$$ where $$f$$ is not differentiable is ___________.

$$ \begin{aligned} &\text { If } \lim _{n \rightarrow \infty} \frac{(n+1)^{k-1}}{n^{k+1}}[(n k+1)+(n k+2)+\ldots+(n k+n)] \\ &=33 \cdot \lim _{n \rightarrow \infty} \frac{1}{n^{k+1}} \cdot\left[1^{k}+2^{k}+3^{k}+\ldots+n^{k}\right] \end{aligned}$$, then the integral value of $$\mathrm{k}$$ is equal to _____________

Let the equation of two diameters of a circle $$x^{2}+y^{2}-2 x+2 f y+1=0$$ be $$2 p x-y=1$$ and $$2 x+p y=4 p$$. Then the slope m $$ \in $$ $$(0, \infty)$$ of the tangent to the hyperbola $$3 x^{2}-y^{2}=3$$ passing through the centre of the circle is equal to _______________.

The sum of diameters of the circles that touch (i) the parabola $$75 x^{2}=64(5 y-3)$$ at the point $$\left(\frac{8}{5}, \frac{6}{5}\right)$$ and (ii) the $$y$$-axis, is equal to ______________.