There are two radioactive substances $A$ and $B$. Decay constant of $B$ is two times that of $A$. Initially, both have equal number of nuclei. After $n$ half lives of $A$, rate of disintegration of both are equal. The value of $n$ is

Two radioactive nuclei $P$ and $Q$, in a given sample decay into a stable nucleolus $R$. 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-