In a $\mathrm{CSTR}$, a homogeneous reaction's first-order of the type $\mathrm{X}\to \mathrm{Y}\to \mathrm{Z}$ (consecutive reaction) is carried out. Among the following, which curve shows a variation of concentration of $\mathrm{X}, \mathrm{Y}$and $\mathrm{Z}$with time?

A substance undergoes a first-order decomposition. The decomposition follows two parallel first-order reactions as given below.

The percentage distributions of $\mathrm{B}$ and $\mathrm{C}$ are

(${\mathrm{k}}_1=1.26\times {10}^{-4} {\mathrm{s}}^{-1}$ and ${\mathrm{k}}_2=3.8\times {10}^{-5} {\mathrm{s}}^{-1}$)

Consider the elementary reaction sequence shown in the figure. Among the following equations, which one is correct?

Inversion of sucrose $\left({\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}\right)$ is the first-order reaction and is studied by measuring the angle of rotation at different intervals of time
.
If $\left({\mathrm{r}}_{\infty }-{\mathrm{r}}_0\right)\equiv \mathrm{a}$ and $\left({\mathrm{r}}_{\infty }-{\mathrm{r}}_{\mathrm{t}}\right)\equiv (\mathrm{a}-\mathrm{x}),$ (where, ${\mathrm{r}}_0, {\mathrm{r}}_1$ and ${\mathrm{r}}_{\infty }$ are the angles of rotation at the start, at the time $\mathrm{t}$ and at the end of the reaction, respectively), then there is $50\%$ inversion when:

Consider the decay of $\mathrm{P}$ to $\mathrm{A}$ and $\mathrm{B}$ by two parallel first-order reactions as shown in the figure

Which of the following is (are) true?