Which of the following is not a mode of radioactive decay

A fresh radioactive sample is given at $t = 0$. Its decay fraction are $\frac{1}{5}$ at $t_1$ instant and $\frac{4}{5}$ at $t_2$ instant. Its mean life is

${C^{14}}$ has half life $5700$ years. At the end of $11400$ years, the actual amount left is

Two radioactive nuclei $A$ and $B$ both convert into a stable nucleus $C$. At time $t = 0$ nuclei of $A$ are $4N_0$ and that of $B$ are $N_0$. Half life of $A$ is $1\, min$ and that of $B$ is $2\, min$. initially number of nuclei of $C$ are zero. At what time rate of disintegrations of $A$ and $B$ are equal ………. $min$

A parent nucleus $X$ is decaying into daughter nucleus $Y$ which in turn decays to $Z$. The half lives of $X$ and $Y$ are $40000 \,yr$ and $20 \,yr$, respectively. In a certain sample, it is found that the number of $Y$ nuclei hardly changes with time. If the number of $X$ nuclei in the sample is $4 \times 10^{20}$, the number of $Y$ nuclei present in it is