Two radioactive materials $X_1$ $X_1$ contain same number of nuclei. If $6\lambda s^{-1}$ and $4\lambda s^{-1}$ are the decay constants of $X_1$ and $X_2$ respectively, the ratio of number of 48 nuclei, undecayed of $X_1$ to that of $X_2$ will be (1/e) after a time.

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 $4N_0$ and that of $Q$ are $N_0.$ Half-life of $P$ (for conversion to $R$) is $1minute$ where as that of $Q$ is $2minutes.$ 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 :