$3.65 \ g$ of $HCl$ is dissolved in $16.2 \ g$ of water. The mole fraction of $HCl$ in the resulting solution is

Which among the following compounds has the highest boiling point?

Which of the following groups is not an auxochrome?

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

In the extraction of aluminium:
Process $X$: applied for red bauxite to remove iron oxide (chief impurity).
Process $Y$: (Serpeck's process) applied for white bauxite to remove $Z$ (chief impurity). Then,process $X$ and impurity $Z$ are:

Let $f(x)$ be a non-negative continuous function such that the area bounded by the curve $y = f(x)$,$x$-axis and the ordinates $x = \frac{\pi}{4}$ and $x = \beta > \frac{\pi}{4}$ is $\left( \beta \sin \beta + \frac{\pi}{4} \cos \beta + \sqrt{2} \beta \right)$. Then $f\left( \frac{\pi}{2} \right)$ is