Which integrated equation is correct for the following $1^{\mathrm{st} }$ order reaction started with only $\mathrm{A}\left(\mathrm{g}\right)$ in a closed rigid vessel?

$\mathrm{A}\left(\mathrm{g}\right)⟶\mathrm{B}\left(\mathrm{g}\right)+\mathrm{C}\left(\mathrm{g}\right)+\mathrm{D}\left(\mathrm{g}\right)$

${\mathrm{P}}_{\mathrm{i}}=$ initial pressure, ${\mathrm{P}}_{\mathrm{t}}=$ total pressure at time $\mathrm{t}$.

The following data were obtained in an experiment on inversion of cane sugar; (a first order kinetics)

The rate constant (in ${\mathrm{second}}^{-1}$) is $[\ln 2=0.693]$

The decomposition of $N_2{O}_5$in chloroform was followed by measuring the volume of O₂ gas evolved : $2N_2{O}_5$($CC{1}_{4 }$)$\to$$2N_2{O}_4$($CC{1}_{4 }$) + $O_2 \left(g\right)$. The maximum volume of $O_{2 }$gasobtained was$100c{m}^3$. In 500 minutes, $90c{m}^3$of $O_{2 }$were evolved. The first order rate constant $\left(in mi{n}^{-1}\right)$ for the disappearance of $N_2{O}_5$is :

For a hypothetical elementary reaction.

where $\frac{{\mathrm{k}}_1}{{\mathrm{k}}_2}=\frac{1}{2}$

Initially, only $2$ moles of $\mathrm{A}$ are present. The total number of moles of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ at the end of $75\%$ of reaction are:

For the following parallel chain reaction , if the sum of the concentration of $\mathrm{B}$ and $\mathrm{C}$ at any time is $2\mathrm{M}$. What will be $[\mathrm{B}{]}_{\mathrm{t}}$ and ${\left[\mathrm{C}\right]}_{\mathrm{t}}$  respectively?