The distance between the lines represented by the equation $4 x^2+4 x y+y^2-6 x-3 y-4=0$ is

If $\mathrm{y}=x^x+x^{\frac{1}{x}}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

If the plane $\frac{x}{3}+\frac{y}{2}-\frac{z}{4}=1$ cuts the co-ordinate axes at points $\mathrm{A}, \mathrm{B}$ and C , then the area of the triangle ABC is

If $\tan ^{-1}\left(\frac{x}{2}\right)+\tan ^{-1}\left(\frac{y}{2}\right)+\tan ^{-1}\left(\frac{z}{2}\right)=\frac{\pi}{2} \quad$ then $x y+y z+z x=$