The plot of the number $(N)$ of undecayed atoms versus activity $(A)$ of a radioactive substance is

The half-life period of a radioactive element $X$ is the same as the mean life time of another radioactive element $Y$. Initially,both of them have the same number of atoms. Then:

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5\, \text{minutes}$. The time (in minutes) at which the activity reduces to half of its initial value is

The rate of disintegration was observed to be $10^{17}$ disintegrations per second when its half-life period is $1445$ years. The original number of particles is:

$A$ piece of bone of an animal from a ruin is found to have $^{14}C$ activity of $12$ disintegrations per minute per gm of its carbon content. The $^{14}C$ activity of a living animal is $16$ disintegrations per minute per gm. How long ago nearly did the animal die? (Given half-life of $^{14}C$ is $t_{1/2} = 5760$ years)

What percentage of original radioactive atoms is left after five half-lives (in $\%$)?