The alkali metals form salt-like hydrides by direct synthesis at elevated temperatures. The thermal stability of these hydrides decreases in which of the following orders?

$A$ stationary wave is represented by $y = 10 \sin \frac{\pi x}{4} \cos 20 \pi t$,where $x$ and $y$ are expressed in $cm$ and $t$ in seconds. The distance between two consecutive nodes is: (in $cm$)

$A$ sample of $0.1 \text{ g}$ of water at $100^{\circ} \text{C}$ and normal pressure $(1.013 \times 10^5 \text{ Nm}^{-2})$ requires $54 \text{ cal}$ of heat energy to convert to steam at $100^{\circ} \text{C}$. If the volume of the steam produced is $167.1 \text{ cc}$,the change in internal energy of the sample is ....... $\text{J}$.

$\sum_{k=1}^{2n+1} (-1)^{k-1} k^2$ is equal to

In $\triangle ABC$,$(a+b+c)\left(\tan \frac{A}{2}+\tan \frac{B}{2}\right)$ is equal to

Which one of the following is a correct set?