The rate of decay $\left(R\right)$ of nuclei in a radioactive sample is plotted against time $\left(t\right)$. Which of the following best represents the resulting curve?

Q. The count rate of nuclear radiation coming from a radiation coming from a radioactive sample containing ¹²⁸I varies with time as follows.

Time t (minute):	0	25	50	75	100
Ctount rate R (109 s−1):	30	16	8.0	3.8	2.0

(a) Plot In (R₀/R) against t. (b) From the slope of the best straight line through the points, find the decay constant λ. (c) Calculate the half-life t_1/2.

Q. A radioactive nuclei $x$ with active nuclei $N\left(t\right)$ at time t decays with decay constant $\lambda$. Let $R=\text{log}\left(\left|\frac{dN}{dt}\right|\right)$ Suppose the experiment starts at $t=0$ and variation of $R$ is plotted against time $t$ as shown.

Q. In an $LR$ circuit connected to a battery, the rate at which energy is stored in the inductor is plotted against time during the growth of the current in the circuit. Which of the following curves best represents the resulting curve?

Q. A radioactive sample consists of two distinct species having the equal number of atoms initially. The mean-life time of one species is $\tau$ and that of the other is $5\tau$. The decay products in both cases are stable. A plot is made of the total number of radioactive nuclei as a function of time. Which of the following figure best represent the form of this plot ?

Q. The rate at which a particular decay process occurs in a radioactive sample, is proportional to the number of radioactive nuclei present. If N is the number of radioactive nuclei present at some instant, the rate of change of N is $\frac{dN}{dt}=-\lambda N$.

At $t=\infty$, which of the following incorrect?