A radioactive sample has an average life of 30ms and is decaying. A...

${T}_{m} = 30ms$
$C = 200\muF$
\dfrac{q}{N} = \dfrac{{Q}_{0}{e}^{- \dfrac{t}{RC}}}{{N}_{0}{e}^{- \lambda, t}} = \dfrac{{Q}_{0}}{{N}_{0}}{e}^{\left(\left(\lambda - \dfrac{1}{RC}\right)\right\}

Since $\dfrac{q}{N}$ is constant hence
$\lambda = \dfrac{1}{RC}$
$R = \dfrac{1}{\lambdaC} = \dfrac{{T}_{m}}{C} = \dfrac{30 \times {10}^{- 3}}{200 \times {10}^{- 6}} = 150Ω$