$A$ radioactive element emits $\alpha$ and $\beta$ particles. Its mean lives for $\alpha$ and $\beta$ decay are $1620$ years and $405$ years,respectively. After how many years will the activity be reduced to $1/4$ of its initial value?

$A$ radioactive sample has an average life of $30 \, ms$ and is decaying. $A$ capacitor of capacitance $200 \, \mu F$ is first charged and later connected with a resistor $R$. If the ratio of charge on the capacitor to the activity of the radioactive sample is fixed with respect to time,then the value of $R$ should be $.... \, \Omega$.

If the decay or disintegration constant of a radioactive substance is $\lambda$,then its half-life and mean life are respectively:

At a given instant,there are $25\%$ undecayed radioactive nuclei in a sample. After $10 \, s$,the number of undecayed nuclei reduces to $6.25\%$. The mean life of the nuclei is...........$ s$.

Two radioactive materials $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

$A$ certain radioactive substance reduces to $25\%$ of its initial value in $16\ days$. Its half-life is .......... $days$.