The approximate value of $\tan ^{-1}(0.999)$ (up to $4$ decimal places) is

Electric current is measured by a tangent galvanometer, where the current is proportional to the tangent of the angle $\theta$ of deflection. If the deflection is read as $45^{\circ}$ and an error of $1 \%$ is made in reading it, then the percentage error in the current is:

Use differentials to approximate $(25)^{\frac{1}{3}}$.

Water is dripping out from a conical funnel of semi-vertical angle $\frac{\pi}{4}$ at the uniform rate of $2 \text{ cm}^2/\text{sec}$ in the surface area,through a tiny hole at the vertex of the bottom. When the slant height of the cone is $4 \text{ cm}$,find the rate of decrease of the slant height of water.

The approximate value of $\sqrt[3]{28}$ rounded up to $3$ decimal places is

Consider the following statements:
$A$ is the relative error in the area of a square when the relative error in its side is $0.4$.
$B$ is the relative error in the volume of a sphere when the relative error in its radius is $0.3$.
$C$ is the relative error in the surface area of a closed cylinder whose height is equal to its radius, when the relative error in its height is $0.2$.
$D$ is the approximate error in $y = x^2 + x - 3$ when $x = 2$ and $\delta x = 0.1$.
The ascending order of the values of errors in these statements is: