At $T(K)$,a gaseous mixture contains $H_2$ and $O_2$. The total pressure of the mixture is $2 \ bar$. The partial pressure of $H_2$ is $1.778 \ bar$. What is the weight $(w/w)$ percentage of $H_2$ in the mixture?

$A + 2B \rightarrow AB_{2}$. $36.0 \ g$ of '$A$' (Molar mass: $60 \ g \ mol^{-1}$) and $56.0 \ g$ of '$B$' (Molar mass: $80 \ g \ mol^{-1}$) are allowed to react. Which of the following statements are correct?
$(A)$ '$A$' is the limiting reagent
$(B)$ $77.0 \ g$ of $AB_{2}$ is formed
$(C)$ Molar mass of $AB_{2}$ is $220 \ g \ mol^{-1}$
$(D)$ $15.0 \ g$ of '$A$' is left unreacted after the completion of reaction.
Choose the correct answer from the options given below:

If $1 \ g$ of each of the following gases are taken at $STP$,which of the gases will occupy $(a)$ greatest volume and $(b)$ smallest volume? $CO, H_2O, CH_4, NO$

If $2.4088 \times 10^{21}$ molecules are removed from $392 \, mg$ of $H_2SO_4$ in a container,the number of $H_2SO_4$ molecules remaining in the container will be ........

What quantity (in $mL$) of a $45\%$ acid solution of a mono-protic strong acid must be mixed with a $20\%$ solution of the same acid to produce $800 \ mL$ of a $29.875\%$ acid solution?

$A$ mixture of sodium oxide $(Na_2O)$ and calcium oxide $(CaO)$ is dissolved in water and saturated with excess carbon dioxide $(CO_2)$ gas. The resulting solution is $......$ It contains $.........$ :