The diameter of a sphere is measured as 42 cm . If there is an error of $1 / 77 \mathrm{~cm}$ in measuring it, then the error involved in the volume of that sphere (in cubic centimeters) is

For $h, k \in N$, let $P(h, k)$ be the point of intersection of the curves $x^2 y-x^3=8$ and $y^3-x y^2=32$. If $\theta$ is the acute angle between these two curves at $P$, then $\tan \theta=$

If the absolute maximum and absolute minimum values of the function $f(x)=x^3-2 x^2+x-3$ defined on $[0,2]$ are $M$ and $m$ respectively, then $M+m=$

If the slope of the tangent drawn at any point $(x, y)$ to the curve $y=f(x)$ is $3 x^2-5$ and $f(1)=2$, then the tangent at $(1,2)$ to the curve $y=f(x)$ intersects the curve at the point