$A$ radioactive substance emits $100$ beta particles in the first $2 \,s$ and $50$ beta particles in the next $2 \,s$. The mean life of the sample is

$A$ count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later,the meter shows a count rate of $30$ per minute. The half-life of the source is .......... $min$.

An active nucleus decays to one-third $\left(\frac{1}{3}\right)$ of its initial activity in $20 \text{ hours}$. The fraction of original activity remaining after $80 \text{ hours}$ is:

The decay constant of a radioisotope is $\lambda$. If its activity at times $t_1$ and $t_2$ are $A_1$ and $A_2$ respectively,then the number of nuclei that have decayed during the time interval $(t_1 - t_2)$ is:

The rate of radioactive disintegration at an instant for a radioactive sample of half-life $2.2 \times 10^9 \; s$ is $10^{10} \; s^{-1}$. The number of radioactive atoms in that sample at that instant is,

In the figure,$X$ represents time and $Y$ represents the activity of a radioactive sample. The activity of the sample varies with time according to which curve?