In Fig. $X$ represents time and $Y$ represent activity of a radioactive sample. Then the activity of sample, varies with time according to the curve

$1 \,mg$ gold undergoes decay with $2.7$ days half-life period, amount left after $8.1$ days is ......... $mg$

The decay constant $\lambda $ of the radioactive sample is the probability of decay of an atom in unit time, then

Which sample, $A$ or $B$ shown in figure has shorter mean-life?

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

If $10\%$ of a radioactive material decays in $5\, days$ then the amount of the original material left after $20\, days$ is approximately .......... $\%$