Which chemical must be applied to the roots to keep the leaves of a plant green?

Let $\overline{a}, \overline{b}$ and $\overline{c}$ be three non-zero vectors such that no two of them are collinear and $(\overline{a} \times \overline{b}) \times \overline{c}=\frac{1}{3}|\overline{b}||\overline{c}| \overline{a}$. If $\theta$ is the angle between the vectors $\overline{b}$ and $\overline{c}$,then the value of $\sin \theta$ is

$A$ function $y = f(x)$ satisfies $(x + 1) f'(x) - 2(x^2 + x) f(x) = \frac{e^{x^2}}{x + 1}$ for all $x > -1$. If $f(0) = 5$,then $f(x)$ is:

Two of the lines represented by the equation $a y^4+b x y^3+c x^2 y^2+d x^3 y+e x^4=0$ will be perpendicular,then

If the excess pressure inside a soap bubble is balanced by an oil column of height $2\; mm$,then the surface tension of the soap solution will be ($r = 1\; cm$ and density $d = 0.8\; g/cm^3$).

In the following sequence of reactions,the alkene affords the compound $B$:
$CH_3-CH=CH-CH_3$ $\xrightarrow{O_3} A$ $\xrightarrow{Zn, H_2O} B$
The compound $B$ is