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

At time $t=0$, a material is composed of two radioactive atoms $A$ and $B$, where $N_{A}(0)=2 N_{B}(0)$. The decay constant of both kinds of radioactive atoms is $\lambda$. However, $A$ disintegrates to $B$ and $B$ disintegrates to $C$. Which of the following figures represents the evolution of $N_{B}(t) / N_{B}(0)$ with respect to time $t$?
$N_{A}(0) = \text{Number of } A \text{ atoms at } t=0$
$N_{B}(0) = \text{Number of } B \text{ atoms at } t=0$

The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

$A$ radioactive substance contains $10000$ nuclei and its half-life period is $20$ days. The number of nuclei present at the end of $10$ days is

$Rn$ decays into $Po$ by emitting an $\alpha$-particle with a half-life of $4 \text{ days}$. $A$ sample contains $6.4 \times 10^{10}$ atoms of $Rn$. After $12 \text{ days}$,the number of atoms of $Rn$ left in the sample will be:

Consider an initially pure $M \text{ g}$ sample of an isotope $X$ with mass number $A$,which has a half-life of $T \text{ hours}$. What is its initial decay rate? ($N_A$ = Avogadro number)