The angle $\theta$, at which the curves $y=3^x$ and $y=7^x$ intersect, is given by

The function $\mathrm{f}(x)=x^3-6 x^2+\mathrm{ax}+\mathrm{b}$ satisfies the conditions of Rolle's theorem in $[1,3]$. Then the values of $a$ and $b$ are respectively

$\mathrm{f}(x)=\frac{x}{2}+\frac{2}{x}, x \neq 0$ is strictly decreasing in

The rate of change of the volume of a sphere with respect to its surface area, when the radius is 5 m is