Let $f(x)=\left\{\begin{array}{cc}1+6 x-3 x^2 & x \leq 1 \\ x+\log _2\left(b^2+7\right) & x>1\end{array}\right.$. Then, the set of all possible values of $b$ such that $f(1)$ is the maximum value of $f(x)$ is

If $\theta$ is the acute angle between the curves $x^2+y^2=4$ and $y^2=3 x$, then $\tan \theta=$

Let $\sqrt{3}$ be the radius and $\frac{\pi}{3}$ be the semi-vertical angle of the given cone. Then, the height of the right circular cylinder of maximum volume that can be inscribed in the given cone is

If an error of $0.02 \mathrm{sq} . \mathrm{cm}$ is found in the surface area of a sphere when its radius is measured as 10 cm , then the approximate error that occurs in the volume of the sphere, in cubic centimeters, is