$A$ single slit of width $0.20 \, mm$ is illuminated with light of wavelength $500 \, nm$. The observing screen is placed $80 \, cm$ from the slit. The width of the central bright fringe will be.....$mm$

If the impurity in a metal has a greater affinity for oxygen and is more easily oxidised than the metal,then the purification of metal may be carried out by

If $Q$ denotes the set of all rational numbers and $f\left(\frac{p}{q}\right)=\sqrt{p^2-q^2}$ for any $\frac{p}{q} \in Q$,then observe the following statements.
$I$. $f\left(\frac{p}{q}\right)$ is real for each $\frac{p}{q} \in Q$
$II$. $f\left(\frac{p}{q}\right)$ is a complex number for each $\frac{p}{q} \in Q$.
Which of the following is correct?

$CHO-(CHOH)_4-CH_2OH \xrightarrow{Br_2/H_2O} P$; $P$ is

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:

The solution of $\frac{dy}{dx} = (\frac{x}{y})^{-1/3}$ is