For the reaction $2NO_2 + F_2 \to 2NO_2F$,the following mechanism has been provided:
$NO_2 + F_2 \xrightarrow{slow} NO_2F + F$
$NO_2 + F \xrightarrow{fast} NO_2F$
Thus,the rate expression of the above reaction can be written as:

The shortest distance between the line $y - x = 1$ and the curve $x = y^2$ is:

$A$ metal crystallises in a face-centred cubic $(FCC)$ structure. If the edge length of its unit cell is $a$,the closest approach between two atoms in the metallic crystal will be:

$A$ hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho$. The sphere is moving horizontally with an acceleration $2g$,where $g$ is the acceleration due to gravity. If the minimum pressure of the liquid is $P_0$,then find the pressure at the centre of the sphere.

The structure of $X$ is

What is obtained from yeast?