If $$y=[(x+1)(2 x+1)(3 x+1) \ldots(\mathrm{n} x+1)]^{\frac{3}{2}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=0$$ is

If $$\cos x+\cos y-\cos (x+y)=\frac{3}{2}$$, then

The joint equation of the lines pair of lines passing through the point $$(3,-2)$$ and perpendicular to the lines $$5 x^2+2 x y-3 y^2=0$$ is

If the line $$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{4}$$ meets the plane $$x+2 y+3 z=15$$ at the point $$P$$, then the distance of $$\mathrm{P}$$ from the origin is