If one starts with $1 \, \text{curie}$ of a radioactive substance $(T_{1/2} = 12 \, \text{hrs})$, the activity left after a period of $1 \, \text{week}$ will be about:

Two radioactive substances $X$ and $Y$ originally have $N_{1}$ and $N_{2}$ nuclei respectively. The half-life of $X$ is half of the half-life of $Y$. After three half-lives of $Y$,the number of nuclei of both are equal. The ratio $\frac{N_{1}}{N_{2}}$ will be equal to:

$A$ radioactive substance in a laboratory has a half-life of $2 \text{ hours}$. It is considered safe for laboratory use when its activity reduces to $1/64$ of its initial value. After how many hours will the laboratory be safe?

Number of nuclei of a radioactive substance at time $t = 0$ are $1000$ and $900$ at time $t = 2 \, s$. Then number of nuclei at time $t = 4 \, s$ will be

$A$ radioactive sample decays $\frac{7}{8}$ times its original quantity in $15$ minutes. The half-life of the sample is $......$ minutes.

Half-life of a radioactive substance is $20 \text{ min}$. The time between $20 \%$ and $80 \%$ decay will be: (in $\text{ min}$)