$A$ radioactive element decays to form a stable nuclide. The rate of decay of the reactant $\left( \frac{dN}{dt} \right)$ will vary with time $(t)$ as shown in which figure?

The activity of a radioactive sample is measured as $N_0$ counts per minute at time $t=0$,and $\frac{N_0}{e}$ counts per minute at time $t=3$ minutes. The activity reduces to half its value in time (in minutes) is:

For a radioactive material,the half-life is $10$ minutes. If initially there are $600$ nuclei,the time taken (in minutes) for the disintegration of $450$ nuclei is:

Two radioactive samples $A$ and $B$ have half-lives $T_1$ and $T_2$ $(T_1 > T_2)$ respectively. At $t=0$,the activity of $B$ was twice the activity of $A$. Their activity will become equal after a time:

At time $t=0$, a material is composed of two radioactive atoms $A$ and $B$, where $N_{A}(0)=2 N_{B}(0)$. The decay constant of both kinds of radioactive atoms is $\lambda$. However, $A$ disintegrates to $B$ and $B$ disintegrates to $C$. Which of the following figures represents the evolution of $N_{B}(t) / N_{B}(0)$ with respect to time $t$?
$N_{A}(0) = \text{Number of } A \text{ atoms at } t=0$
$N_{B}(0) = \text{Number of } B \text{ atoms at } t=0$

In a radioactive material,the activity at time $t_1$ is $R_1$ and at a later time $t_2$ it is $R_2$. If the decay constant of the material is $\lambda$,then: