Let a random variable $X$ have a binomial distribution with mean $8$ and variance $4$. If $P(X \le 2) = \frac{k}{2^{16}}$,then $k$ is equal to

If $\frac{x-4}{x^2-5x-2k} = \frac{2}{x-2} - \frac{1}{x+k}$,then $k$ is equal to

Observe the following statements :
$I$. Bleaching powder is used in the preparation of chloroform.
$II$. Bleaching powder decomposes in the presence of $CoCl_2$ to liberate $O_2$.
$III$. Aqueous $KHF_2$ is used in the preparation of fluorine.
The correct combination is :

Which science presents the changes in the internal and external structure of plants from the perspective of evolution and phylogeny?

If for some $\alpha \in R$,the lines $L_{1}: \frac{x+1}{2}=\frac{y-2}{-1}=\frac{z-1}{1}$ and $L_{2}: \frac{x+2}{\alpha}=\frac{y+1}{5-\alpha}=\frac{z+1}{1}$ are coplanar,then the line $L_{2}$ passes through the point

If $z_1, z_2$ are two complex numbers satisfying $\left|\frac{z_1-3 z_2}{3-z_1 \bar{z}_2}\right|=1$ and $\left|z_1\right| \neq 3$,then $\left|z_2\right|$ is equal to