The graph between the instantaneous concentration $(N)$ of a radioactive element and time $(t)$ is:

The half-life of a radioactive isotope $x$ is $50$ years. It decays to another element $y$ which is stable. The two elements $x$ and $y$ were found to be in the ratio of $1 : 7$ in a sample of a given rock. The age of the rock was estimated to be ........... $years$.

The activity of a sample reduces from $A_0$ to $A_0 / \sqrt{3}$ in one hour. The activity after $3$ hours more will be

The half-life of a radioactive element is $10 \, days$. The time required for the mass of the sample to reduce to $\frac{1}{10}$ of its initial mass is approximately ........ days.

In a sample of $^{66}Cu$,$7/8$ of the initial number of nuclei decay into $Zn$ in $15 \ min$. The half-life of the sample is ......... $min$.

The nuclide $^{131}I$ is radioactive,with a half-life of $8.04$ days. At noon on January $1$,the activity of a certain sample is $600 \, Bq$. The activity at noon on January $24$ will be