For a first order reaction a graph is plotted between $\log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}$(y-axis)  vs time in minutes(x-axis). If the slope of the graph is $0.1$ then the half life of the reaction will be

$\begin{array}{l}\mathrm{K}\hspace{0.17em}=\mathrm{\hspace{0.17em}}\frac{2.303}{\mathrm{t}}\log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}\\ \hspace{0.17em}\log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}\hspace{0.17em}=\hspace{0.17em}\frac{\mathrm{Kt}}{2.303}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\\ \mathrm{y}=\mathrm{mx}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\\ \mathrm{slope}\hspace{0.17em}\hspace{0.17em}=\mathrm{\hspace{0.17em}}\frac{\mathrm{K}}{2.303}\\ \frac{\mathrm{K}}{2.303}\mathrm{\hspace{0.17em}}=\mathrm{\hspace{0.17em}}0.1\left(\mathrm{given}\right)\\ \mathrm{K}\hspace{0.17em}=\mathrm{\hspace{0.17em}}0.2303\mathrm{\hspace{0.17em}}{\min }^{-1}\\ {\mathrm{t}}_{\frac{1}{2}\mathrm{\hspace{0.17em}}}\mathrm{\hspace{0.33em}}=\mathrm{\hspace{0.17em}}\frac{0.693}{0.2303}\mathrm{minutes}\\ {\mathrm{t}}_{\frac{1}{2}\mathrm{\hspace{0.17em}}}\mathrm{\hspace{0.33em}}=\mathrm{\hspace{0.17em}}\frac{0.693}{0.2303}\times 60\mathrm{seconds}\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}180\mathrm{seconds}\end{array}$