The rate of disintegration of a radioactive sample is $R$ and the number of atoms present at any time $t$ is $N$. When $\frac{R}{N}$ is taken along the $Y$-axis and $t$ is taken along the $X$-axis,the correct graph is:

$A$ sample contains $10^{-2} \ kg$ each of two substances $A$ and $B$ with half-lives $4 \ s$ and $8 \ s$ respectively. The ratio of their atomic weights is $1:2$. The ratio of the amounts (number of atoms) of $A$ and $B$ remaining after $16 \ s$ is $\frac{x}{100}$. The value of $x$ is:

The masses of two radioactive substances are same and their half-lives are $1 \ yr$ and $2 \ yr$ respectively. The ratio of their activities after $4 \ yr$ will be

$A$ radioactive element decays to form a stable nuclide. The graph representing the number of radioactive nuclei $(N)$ versus time $(t)$ is:

The half-life of a radioactive nuclide is

In a radioactive decay process,the activity is defined as $A = -\frac{dN}{dt}$,where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources,$S_1$ and $S_2$,have the same activity at time $t = 0$. At a later time,the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$,respectively. When $S_1$ and $S_2$ have just completed their $3^{\text{rd}}$ and $7^{\text{th}}$ half-lives,respectively,the ratio $A_1/A_2$ is: