Rate constant of a reaction is  $10 \mathrm{lit} {\mathrm{mole}}^{-1} {\min }^{-1}$. Then the correct relation between half life and initial concentration for the reaction is

Units of K are  $\mathrm{lit}. {\mathrm{mole}}^{-1} {\min }^{-1}$
General units of ‘K’ =  ${\left(\mathrm{mole}/\mathrm{lit}\right)}^{1-\mathrm{n}}{\mathrm{time}}^{-1}$
${\mathrm{mole}}^{1-\mathrm{n}}{\mathrm{lit}}^{\mathrm{n}-1}{\mathrm{time}}^{-1}={\mathrm{mole}}^{-1}{\mathrm{litmin}}^{-1}$

n = 2
it is a second order reaction
General condition
$\begin{array}{l} {\mathrm{t}}_{\frac{1}{2}}\propto {\mathrm{a}}^{1-\mathrm{n}}\\ \mathrm{thus} {\mathrm{t}}_{\frac{1}{2}}\propto \frac{1}{\mathrm{a}}\end{array}$