$x$ fraction of a radioactive sample decays in $t$ time. What fraction will decay in $2t$ time?

In a radioactive substance at $t = 0$,the number of atoms is $8 \times 10^4$. Its half-life period is $3 \ years$. The number of atoms $1 \times 10^4$ will remain after an interval of ........... $years$.

$A$ radioactive element of mass $1 \,kg$ after $N$ years is left with only $125 \,g$. If the half-life of the element is $12.5 \,y$, then the value of $N$ is:

The half-life of a radioactive substance is $30 \text{ minutes}$. The time taken between $40 \%$ decay and $85 \%$ decay of the same radioactive substance is

The rate of disintegration of a radioactive sample is $R$ and the number of atoms present at any time $t$ is $N$. When $\frac{R}{N}$ is taken along the $Y$-axis and $t$ is taken along the $X$-axis,the correct graph is:

The radioactivity of a sample at time $T_1$ is $R_1$ and at time $T_2$ is $R_2$. If the mean life of the sample is $T$,then the number of nuclei disintegrated in the time interval $(T_2 - T_1)$ is: