Two radioactive samples $A_1$ and $A_2$ have decay constants $10\lambda_0$ and $\lambda_0$ respectively. If they initially contain the same number of nuclei,find the ratio of the number of undecayed nuclei after time $t = 1/(9\lambda_0)$.

$A$ radioactive element decays to form a stable nuclide. The graph representing the number of radioactive nuclei $(N)$ versus time $(t)$ is:

The decay constant of radium is $\lambda$. By a suitable process,its compound radium bromide is obtained. The decay constant of radium bromide will be:

$A$ radioactive material of half-life $T$ was kept in a nuclear reactor at two different instants. The quantity kept the second time was twice that kept the first time. If their present activities are $A_1$ (first) and $A_2$ (second) respectively,then their age difference is equal to:

Two radioactive nuclei $P$ and $Q$ in a given sample decay into a stable nucleus $R.$ At time $t = 0,$ the number of $P$ species is $4N_0$ and that of $Q$ is $N_0.$ The half-life of $P$ is $1 \text{ minute},$ while that of $Q$ is $2 \text{ minutes}.$ Initially,there are no nuclei of $R$ present in the sample. When the number of nuclei of $P$ and $Q$ are equal,the number of nuclei of $R$ present in the sample would be

Two radioactive nuclei $A$ and $B$ both convert into a stable nucleus $C$. At time $t = 0$,the number of nuclei of $A$ is $4N_0$ and that of $B$ is $N_0$. The half-life of $A$ is $1 \, min$ and that of $B$ is $2 \, min$. Initially,the number of nuclei of $C$ is zero. At what time are the rates of disintegration of $A$ and $B$ equal?