For the given sequential reaction $A\;\overset{k_1} \rightarrow \;B\;\overset{k_2} \rightarrow C$ the concentration of A,B & C at any time 't' is given by $[A]_t=[A]_oe^{-k_1t};[B]_t=\large\frac{k_1[A_o]}{k_2-k_1}$$[e^{-k_1t}-e^{-k_2t}];[C]_t=[A_o]-([A]_t-([A]_t+[B]_t)$.The maximum concentration of $[B]$ is

Question

$\begin{array}{1 1}(a)\;\large\frac{k_1[A_o]}{k_2-k_1}\bigg[\normalsize e^{\big(k_1/k_1-k_2\;ln\large\frac{k_1}{k_2}\big)}-e^{\big(k_2/k_1-k_2\;ln\large\frac{k_1}{k_2}\big)}\bigg]\\(b)\;\large\frac{k_1[A_o]}{k_2-k_1}\bigg[\normalsize e^{\big(k_1/k_2-k_1\;ln\large\frac{k_1}{k_2}\big)}-e^{\big(k_2/k_2-k_1\;ln\large\frac{k_1}{k_2}\big)}\bigg]\\(c)\;\large\frac{k_1[A_o]}{k_1-k_2}\bigg[\normalsize e^{\big(k_1/k_1-k_2\;ln\large\frac{k_1}{k_2}\big)}+e^{\big(k_2/k_1-k_2\;ln\large\frac{k_1}{k_2}\big)}\bigg]\\(d)\;\large\frac{k_1[A_o]}{k_1-k_2}\bigg[\normalsize e^{\big(k_1/k_1-k_2\;ln\large\frac{k_1}{k_2}\big)}-e^{\big(k_2/k_1-k_2\;ln\large\frac{k_1}{k_2}\big)}\bigg]\end{array}$