$A$ 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 $\mu Ci$?

Two radioactive elements $A$ and $B$ initially have the same number of atoms. The half-life of $A$ is equal to the mean life of $B$. If $\lambda_A$ and $\lambda_B$ are the decay constants of $A$ and $B$ respectively,then choose the correct relation from the given options.

An element used for radioactive carbon dating for more than $5600$ years is

$A$ solution containing active cobalt ${}_{27}^{60}Co$ having activity of $0.8\,\mu Ci$ and decay constant $\lambda$ is injected into an animal's body. If $1\,cm^3$ of blood is drawn from the animal's body after $10\,hrs$ of injection,the activity found is $300\,decays$ per minute. What is the total volume of blood in the animal's body in litres? (Given: $1\,Ci = 3.7 \times 10^{10}$ decays per second and at $t = 10\,hrs$,$e^{-\lambda t} = 0.84$)

The half-life of the isotope $_{11}Na^{24}$ is $15 \, hrs$. How much time does it take for $\frac{7}{8}$ of a sample of this isotope to decay?

Half-lives of two radioactive nuclei $A$ and $B$ are $10 \, minutes$ and $20 \, minutes$,respectively. If,initially,a sample has an equal number of nuclei,then after $60 \, minutes$,the ratio of the number of decayed nuclei of $A$ and $B$ will be: