Water is considered to be polluted if the dissolved oxygen $(D.O.)$ content is less than ... $ppm$ :

$x = \log \left( \frac{1}{y} + \sqrt{1 + \frac{1}{y^2}} \right) \Rightarrow y$ is equal to

$Assertion (A)$: van der Waals' forces are responsible for chemisorption. $Reason (R)$: High temperature is favourable for chemisorption. The correct answer is

If $x^2 y - x^3 \frac{dy}{dx} = y^4 \cos x$, then $x^3 y^{-3}$ is equal to

Which of the following is $NOT$ included in $In-situ$ conservation?

$A$ circular disc of radius $R$ is removed from a bigger uniform circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is