There is a possible error of 0.02 cm in measuring the base diameter of a right circular cone as 14 cm . If the semi-vertical angle of the cone is $45^{\circ}$, then the approximate error in its volume is (in $\mathrm{cu} . \mathrm{cm}$ )

The real valued function $f(x)=\frac{x^2}{2}-\log \left(x^2+x+1\right)$ is

If $x$ and $y$ are two positive real numbers such that $x y=4$, then the minimum value of $\left(\sqrt{x}+\frac{y^2}{2}\right)$ is

If the tangent and the normal drawn to the curve $x y^2+x^2 y=12$ at the point $(1,3)$ meet the X -axis in $T$ and $N$ respectively, then $T N=$