The ratio of ${\mathrm{C}}^{14}$ to ${\mathrm{C}}^{12}$ in a living matter is measured to be $\frac{{\mathrm{C}}^{14}}{{\mathrm{C}}^{12}}=1.3\times {10}^{-12}$ at the present time.

Activity of $12.0\mathrm{gm}$ carbon sample is $180 \mathrm{dpm}$. The half of ${\mathrm{C}}^{14}$ is nearly _____$\times {10}^{12}$sec. [Given: ${\mathrm{N}}_{\mathrm{A}}=6\times {10}^{23}$]

Read the following:

(i) The half-life period of a radioactive element $\mathrm{X}$ is same as the mean-life time of another radioactive element $\mathrm{Y}$. Initially both of them have the same number of atoms. Then $\mathrm{Y}$ will decay at a faster rate than $\mathrm{X}$.

(ii) The electron emitted in beta radiation originates from decay of a neutron in a nucleus.

(iii) The half-life of ${}^{215}\mathrm{At}$ is $100\mathrm{ms}$. The time taken for the radioactivity of a sample of ${}^{215}\mathrm{At}$ to decay to $1/16\mathrm{th}$ of its initial value is $400\mathrm{ms}$.

(iv) The volume $\left(\mathrm{V}\right)$ and mass $\left(\mathrm{m}\right)$ of a nucleus are related as $\mathrm{V}\propto \mathrm{m}$.

(v) Given a sample of Radium $-226$ having half-life of $4 \mathrm{days}$. The probability, a nucleus disintegrates within $2$ half lives is $3/4$

Select the correct code for above.