If the variance of the numbers $$-1,0,1, \mathrm{k}$$ is 5, where $$\mathrm{k} > 0$$, then $$\mathrm{k}$$ is equal to

The differential equation $$\cos (x+y) \mathrm{d} y=\mathrm{d} x$$ has the general solution given by

The area of the region bounded by the curves $$y=\mathrm{e}^x, y=\log x$$ and lines $$x=1, x=2$$ is

If $$x=-1$$ and $$x=2$$ are extreme points of $$\mathrm{f}(x)=\alpha \log x+\beta x^2+x, \alpha$$ and $$\beta$$ are constants, then the value of $$\alpha^2+2 \beta$$ is