JEE Advanced 2015 · Paper 2, Physics question 5

For a radioactive material, its activity $A$ and rate of change of its activity $R$ are defined as $A=-\dfrac{dN}{dt}$ and $R=-\dfrac{dA}{dt}$, where $N(t)$ is the number of nuclei at time $t$. Two radioactive sources $P$ (mean life $\tau$) and $Q$ (mean life $2\tau$) have the same activity at $t=0$. Their rates of change of activities at $t=2\tau$ are $R_P$ and $R_Q$, respectively. If $\dfrac{R_P}{R_Q}=\dfrac ne$, then the value of $n$ is