The activity of a radioactive substance can be represented by various units. Select the correct option.

The mean lives of a radioactive sample are $30$ years and $60$ years for $\alpha$-emission and $\beta$-emission respectively. If the sample decays by both $\alpha$-emission and $\beta$-emission simultaneously,the time after which only one-fourth of the sample remains is:

There are three lumps of a given radioactive substance. Their activity is in the ratio of $1 : 2 : 3$ now. What will be the ratio of their activities at any further date?

The half-life $(T)$ and the disintegration constant $(\lambda)$ of a radioactive substance are related as:

The half-life of a radioactive sample undergoing $\alpha$-decay is $1.4 \times 10^{17} \; s$. If the number of nuclei in the sample is $2.0 \times 10^{21}$,the activity of the sample is nearly:

The number of atoms of a radioactive substance of half-life $T$ is $N_{0}$ at $t=0$. The time necessary to decay from $N_{0} / 2$ atoms to $N_{0} / 10$ atoms will be