The wavelengths of light used in an optical instrument are ${\lambda _1} = 4000\,\mathring{A}$ and ${\lambda _2} = 5000\,\mathring{A}$. The ratio of their respective resolving powers (corresponding to ${\lambda _1}$ and ${\lambda _2}$) is:

In Young's double slit experiment,if the slit widths are in the ratio $1 : 9$,then the ratio of the intensity at minima to that at maxima will be

If $\int_{-1}^{4} f(x) \, dx = 4$ and $\int_{2}^{4} (3 - f(x)) \, dx = 7$,then the value of $\int_{2}^{-1} f(x) \, dx$ is

Let $f: R \to R$,$f(x) = \max \{ |\tan^{-1} x|, \cot^{-1} x \}$. Consider the following statements:
$I$. The function is continuous and derivable $\forall x \in R$.
$II$. The range of the function is $[\frac{\pi}{4}, \pi]$.
$III$. $f(x)$ is many-one into.
Identify the correct option.

If the $B-H$ curves of two samples of $P$ and $Q$ of iron are as shown below, then which one of the following statements is $CORRECT$?

Which of the following is the strongest oxidizing agent?