If the lines $$\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z-3}{\alpha}$$ and $$\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{\beta}$$ intersect, then the magnitude of the minimum value of $$8 \alpha \beta$$ is _____________.

If

$$(20)^{19}+2(21)(20)^{18}+3(21)^{2}(20)^{17}+\ldots+20(21)^{19}=k(20)^{19}$$,

then $$k$$ is equal to ___________.

The number of points, where the curve $$y=x^{5}-20 x^{3}+50 x+2$$ crosses the $$\mathrm{x}$$-axis, is ____________.

A particle starts with an initial velocity of $$10.0 \mathrm{~ms}^{-1}$$ along $$x$$-direction and accelerates uniformly at the rate of $$2.0 \mathrm{~ms}^{-2}$$. The time taken by the particle to reach the velocity of $$60.0 \mathrm{~ms}^{-1}$$ is __________.