$C^{14}$ has a half-life of $5700$ years. At the end of $11400$ years,the actual amount left is:

In time $t$,$7/8$ of a radioactive sample disintegrates. How much time will it take for $15/16$ of the sample to disintegrate?

Half-lives of two radioactive elements $A$ and $B$ are $30 \text{ minute}$ and $60 \text{ minute}$ respectively. Initially,the samples have an equal number of nuclei. After $120 \text{ minute}$,the ratio of the number of decayed nuclei of $B$ to that of $A$ will be:

Which one of the following nuclei has a shorter mean life?

The half-life of a radioactive substance is $20 \ min$. The time taken for the decay to increase from $20\%$ to $80\%$ is ........ $min$.

$A$ radioactive element decays to form a stable nuclide. The graph representing the number of radioactive nuclei $(N)$ versus time $(t)$ is: