For a reaction \(2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{P}\), when concentration of \(\mathrm{B}\) alone is doubled, \(\frac{\mathrm{t}_{1}}{2}\) does not change and when concentrations of both \(A\) and \(B\) is doubled, rate increases by a factor of 4 . The unit of rate constant is,
(A) \(\mathrm{s}^{-1}\)
(B) \(\mathrm{L} \mathrm{mol}^{-1} \mathrm{~S}^{-1}\)
(C) \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\)
(D) \(\mathrm{L}^{2} \mathrm{~mol}^{-2} \mathrm{~s}^{-1}\)