A radio-isotope has a half- life of $5$ years. The fraction of the atoms of this material that would decay in $15$ years will be

If $20\, gm$ of a radioactive substance due to radioactive decay reduces to $10 \,gm$ in $4 \,minutes,$ then in what time $80\, gm $ of the same substance will reduce to $10 \,gm$

Assertion : ${}^{90}Sr$ from the radioactive fall out from a nuclear bomb ends up in the bones of human beings through the milk consumed by them. It causes impairment of the production of red blood cells.

Reason : The energetic $\beta  – $ particles emitted in the decay of  ${}^{90}Sr$ damage the bone marrow

In Fig. $X$ represents time and $Y$ represent activity of a radioactive sample. Then the activity of sample, varies with time according to the curve

A radioactive nucleus $A$ has a single decay mode with half-life $\tau_A$. Another radioactive nucleus $B$ has two decay modes $1$ and $2$. If decay mode $2$ were absent, the half-life of $B$ would have been $\tau_A / 2$. If decay mode $1$ were absent, the half-life of $B$ would have been $3 \tau_A$. If the actual half life of $B$ is $\tau_B$, then the ratio $\tau_B / \tau_A$ is