The network shown in the figure is part of a complete circuit. If at a certain instant,the current $I$ is $5 \ A$ and it is decreasing at a rate of $10^3 \ A \ s^{-1}$,and if $I$ is reversed in direction,then $V_B - V_A$ equals .......... $V$.

Match the following columns correctly:

Column-$I$	Column-$II$
$A$. Tapetum	$i$. Degenerates during development
$B$. Intine	$ii$. Resistant organic material
$C$. Vegetative cell	$iii$. Pollen tube
$D$. Sporopollenin	$iv$. Provides nourishment to pollen grains

Who is known as the Father of Botany?

For any integer $n \geq 1$,the sum $\sum_{k=1}^n k(k+2)$ is equal to

Two polaroids are placed in the path of an unpolarized beam of intensity $I_0$ such that no light is emitted from the second polaroid. If a third polaroid,whose polarization axis makes an angle $\theta$ with the polarization axis of the first polaroid,is placed between these polaroids,then the intensity of light emerging from the last polaroid will be:

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.