The ratio activity of an element becomes $\frac{{1}}{{64}} th$ of its original value in $60\, sec$. Then the half life period is …………$sec$

A sample of radioactive element containing $4 \times 10^{16}$ active nuclei. Half life of element is $10$ days, then number of decayed nuclei after $30$ days is  …….. $\times 10^{16}$ 

Two radioactive elements $R$ and $S$ disintegrate as
$R \rightarrow P + \alpha; \lambda_R = 4.5 × 10^{-3} \,\, years^{-1}$
$S \rightarrow P + \beta; \lambda_S = 3 × 10^{-3} \,\, years^{-1}$
Starting with number of atoms of $R$ and $S$ in the ratio of $2 : 1,$ this ratio after the lapse of three half lives of $R$ will be :

The half life period of a radioactive substance is 60 days. The time taken for $\frac{7}{8}$ th of its original mass to disintegrate will be $……days$ 

A piece of bone of an animal from a ruin is found to have $^{14}C$ activity of $12$ disintegrations per minute per gm of its carbon content. The $^{14}C$ activity of a living animal is $16$ disintegrations per minute per gm. How long ago nearly did the animal die? …………$years$ (Given halflife of $^{14}C$ is $t_{1/2} = 5760\,years$ )