The activity of a radioactive sample

Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is

$\mathop {^{38}S}\limits_{sulpher} \xrightarrow[{ - 2.48\,h}]{{half\,year}}\mathop {^{38}Cl}\limits_{chloride} \xrightarrow[{ - 0.62\,h}]{{half\,year}}\mathop {^{38}Ar}\limits_{Argon} $ 

Assume that we start with $1000$ $^{38}S$ nuclei at time $t = 0$. The number of $^{38} Cl$ is of count zero at $ t=0$ an will again be zero at $t = \infty $. At what value of $t,$ would the number of counts be a maximum ?

Two radioactive materials $X_1$ and $X_2$ have decay constant $5\lambda$ and $\lambda$ respectively intially they have the saame number of nuclei, then the ratio of the number of nuclei of $X_1$ to that $X_2$ will be $\frac{1}{e}$ after a time

Give the equation form of exponential law. 

$99 \%$ of a radioactive element will decay between

The ratio activity of an element becomes $\frac{{1}}{{64}} th$ of its original value in $60\, sec$. Then the half life period is ............$sec$