In a Ruby laser, the colour of laser light is due to ______ atom.

The work functions of metals $A$ and $B$ are in the ratio $1 : 2$. If light of frequencies $f$ and $2f$ are incident on the surfaces $A$ and $B$ respectively,the ratio of the maximum kinetic energy of photoelectrons emitted is ($f$ and $2f$ are both frequencies greater than the threshold frequency of metals $A$ and $B$ respectively).

In the following compounds,the order of acidity is:
$(I)$ Phenol
$(II)$ $p$-Cresol ($4$-methylphenol)
$(III)$ $m$-Nitrophenol
$(IV)$ $p$-Nitrophenol

The fossil bone has a ${}^{14}C:{}^{12}C$ ratio,which is $\left( \frac{1}{16} \right)$ of that in a living animal bone. If the half-life of ${}^{14}C$ is $5730 \text{ years}$,then the age of the fossil bone is ......... $\text{years}$.

The value of $k$ for which the equation $x^2-4xy-y^2+6x+2y+k=0$ represents a pair of straight lines is equal to ........

The binding energies of nuclei $X$ and $Y$ are $E_1$ and $E_2$ respectively. Two atoms of $X$ are fused to give one atom of $Y$ and an energy $Q$ is released. Then