$A$ radioactive sample of half-life $ 10 $ days contains $ 1000x $ nuclei. The number of original nuclei present after $ 5 $ days is: (in $x$)

The half-life of $_{38}^{90} Sr$ is $28$ years. What is the disintegration rate of $15 \; mg$ of this isotope?

In a radioactive sample,there are $1.414 \times 10^6$ active nuclei. If they reduce to $10^6$ within $10 \text{ min}$,then the half-life of this sample will be ....... $\text{min}$.

$A$ radioactive sample with a half-life of $1$ month has the label: "Activity $= 2 \, \mu Ci$ on $1-8-1991$." What will be its activity two months earlier in $\mu Ci$?

The activity of a radioactive material is $2.56 \times 10^{-3} \, Ci$. If the half-life of the material is $5 \, \text{days}$, after how many days will the activity become $2 \times 10^{-5} \, Ci$?

At $t = 0$,the number of active nuclei in a sample is $N_0$. How many nuclei will decay in the time interval between its first mean life and second half-life?