$A$ radioactive sample has a half-life of $5$ years. The probability of decay in $10$ years will be ........$\%$

The decay constants of two radioactive elements are $15x$ and $3x$ respectively. Initially,they have the same number of nuclei. After a time of $\frac{1}{6x}$,the ratio of the number of their nuclei will be ........

The half-life period of a radioactive element $X$ is the same as the mean life time of another radioactive element $Y$. Initially,both of them have the same number of atoms. Then:

$A$ sample of living carbon-containing matter has an activity of $15$ decays/minute per gram of carbon-$14$. $A$ sample from the Indus Valley civilization has an activity of $9$ decays/minute per gram of carbon-$14$. Given the half-life of $C^{14}$ is $5730$ years, find the age of the Indus Valley civilization.

The half-life of a radioactive substance is $T$. The time taken for disintegrating $\frac{7}{8}$th part of its original mass will be

The half-life period of a radioactive element $A$ is $62 \text{ years}$. It decays into another stable element $B$. An archaeologist found a sample in which $A$ and $B$ are in $1 : 15$ ratio. The age of the sample is (in $\text{ years}$)