The correct order of the $O-O$ bond length in $O_2$,$H_2O_2$ and $O_3$ is

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

For a binomial variate $X$ with $n=6$,if $P(X=2)=9 P(X=4)$,then its variance is

Feeling the tremors of an earthquake,a scared resident of the seventh floor of a multistoreyed building starts climbing down the stairs rapidly. Which hormone initiates this action?

The point of contact of the circles $x^2+y^2+2x+2y+1=0$ and $x^2+y^2-2x+2y+1=0$ is

If $l$ and $m$ are the degree and the order respectively of the differential equation of the family of all circles in the $XY$ plane with radius $5$ units,then $2l + 3m =$