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

Time $\left(\min \right)$	$0$	$10$	After a long time
Total angle of rotation (degree)	$+40$	$+15$	$-10$

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?