Acidified potassium permanganate solution is decolourised by

$A$ function $y = f(x)$ is given by $x = \frac{1}{1 + t^2}$ and $y = \frac{1}{t(1 + t^2)}$ for all $t > 0$. Then $f$ is:

Two particles $A$ and $B$ of masses $m$ and $2m$ are suspended from massless springs of force constants $K_1$ and $K_2$. During their oscillation,if their maximum velocities are equal,then the ratio of amplitudes of $A$ and $B$ is

The radius of the circle $r = 12 \cos \theta + 5 \sin \theta$ is

In which of the following arrangements is the order $NOT$ according to the property indicated against it?

Columella auris is a modified