The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half-life of the radioactive sample is

$A$ sample of radioactive material $A$,which has an activity of $10\, mCi$ $(1\, Ci = 3.7 \times 10^{10}\, \text{decays/s})$,has twice the number of nuclei as another sample of different radioactive material $B$,which has an activity of $20\, mCi$. The correct choices for half-lives of $A$ and $B$ would then be respectively:

The activity of a radioactive sample decreases to $\left(\frac{1}{3}\right)$ of its original value in $3 \ days$. Then,in $9 \ days$,its activity reduces to:

The half-life of radium is $1620$ years and its atomic weight is $226 \ kg/kmol$. The number of atoms that will decay from its $1 \ g$ sample per second will be (Avogadro's number $N_A = 6.02 \times 10^{26} \ atoms/kmol$)

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

The counting rate observed from a radioactive source at $t = 0$ was $1600 \ counts \ s^{-1}$,and at $t = 8 \ s$,it was $100 \ counts \ s^{-1}$. The counting rate observed as $counts \ s^{-1}$ at $t = 6 \ s$ will be