What fraction of a radioactive material will get disintegrated in a period of two half-lives

Draw a graph showing the variation of decay rate with number of active nuclei. 

Two radioactive nuclei $P$ and $Q,$ in a given sample decay into a stable nucleus $R.$ At time $t = 0,$ number of $P$ species are $4\,\, N_0$ and that of $Q$ are $N_0$. Half-life of $P$ (for conversion to $R$) is $1$ minute where as that of $Q$ is $2$ minutes. Initially there are no nuclei of $R$ present in the sample. When number of nuclei of $P$ and $Q$ are equal, the number of nuclei of $R$ present in the sample would be

Two radioactive materials $A$ and $B$ have decay constants $10\,\lambda $ and $\lambda $, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of $B$ will be $1/e$ after a time

A freshly prepared radioactive sample of half- life $1$ hour emits radiations that are $128$ times as intense as the permissible safe limit. The minimum time after which this sample can be safely used is .........$hours$

The radioactive sources $A$ and $B$ have half lives of $2\ hr$ and $4\ hr$  espectively, initially contain the same number of radioactive atoms. At the end of $2\  hours$, their rates of distintegration are in the ratio