$\mathrm{Zn}+2{\mathrm{H}}^{\oplus }⟶{\mathrm{Zn}}^{2+}+{\mathrm{H}}_2$
The half life period is independent of the concentration of zinc at constant pH. For the constant concentration of Zn. the rate becomes 100 times when pH is decreased from 3 to 2. Hence

i) Since t_1/2 is independent of concentration of Zn at constant pH means that the order w.r.t [Zn] = 1
$\text{ ii) Let }{\mathrm{r}}_1\propto {\left[{\mathrm{H}}^{\oplus }\right]}^{\mathrm{x}}$
$$\begin{gathered} {\mathrm{r}}_1\propto {\left[{10}^{-3}\right]}^{\mathrm{x}}[\text{ when }\mathrm{pH}=3] \\ {\mathrm{r}}_2=100{\mathrm{r}}_1\propto {\left[{10}^{-2}\right]}^{\mathrm{x}} [\text{ when }\mathrm{pH}=2] \\ \text{ Thus, }\frac{{\mathrm{r}}_2}{{\mathrm{r}}_1}={\left[\frac{{10}^{-2}}{{10}^{-3}}\right]}^{\mathrm{x}};100={\left(10\right)}^2=[10{]}^{\mathrm{x}} \\ \mathrm{x}=2; \mathrm{Henceorderw}.\mathrm{r}.\mathrm{t}. \left[{\mathrm{H}}^{\oplus }\right]=2 \\ \mathrm{b})\mathrm{Hence},\mathrm{therate} =\left(\frac{\mathrm{dx}}{\mathrm{dt}}\right)=\mathrm{k}\left[\mathrm{Zn}\right]{\left[{\mathrm{H}}^{\oplus }\right]}^2. \\ \mathrm{So} \left(\mathrm{b}\right) \mathrm{is} \mathrm{the} \mathrm{correct} \mathrm{answer} \\ \mathrm{c}) \left(\frac{\mathrm{dx}}{\mathrm{dt}}\right)={\mathrm{r}}_1=\mathrm{k}\left[\mathrm{Zn}\right]{\left[{\mathrm{H}}^{\oplus }\right]}^2;{\mathrm{r}}_2=\mathrm{k}\left[\mathrm{Zn}\right]{\left[\frac{{\mathrm{H}}^{\oplus }}{2}\right]}^2 \\ \mathrm{Thus}, {\mathrm{r}}_2={\mathrm{r}}_1 \\ \mathrm{d}) {\mathrm{r}}_1=\mathrm{k}\left[\mathrm{Zn}\right]{\left[{\mathrm{H}}^{\oplus }\right]}^2;{\mathrm{r}}_2=\mathrm{k}\left[\mathrm{Zn}\right]{\left[2{\mathrm{H}}^{\oplus }\right]}^2 \\ \mathrm{Divide}\left(\mathrm{ii}\right)\mathrm{by}(\mathrm{i}) {\mathrm{r}}_2=4{\mathrm{r}}_1 \end{gathered}$$