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

A mixture consists of two radioactive material $A_1$ and $A_2$ with half lives of $20\,s$ and $10\,s$ respectively . Initially the mixture has $40\,g$ of $A_1$ and $160\,g$ of $A_2$ . The amount of the two in the mixture will become equal after……….$sec$

The decay constant $\lambda $ of the radioactive sample is the probability of decay of an atom in unit time, then

At a given instant, say $t = 0,$ two radioactive substances $A$ and $B$ have equal activates. The ratio $\frac{{{R_B}}}{{{R_A}}}$ of their activities. The ratio $\frac{{{R_B}}}{{{R_A}}}$ of their activates after time $t$ itself decays with time $t$ as $e^{-3t}.$ If the half-life of $A$ is $ln2,$ the half-life of $B$ is

If $10\%$ of a radioactive material decays in $5$ days, then the amount of original material left after $20$ days is approximately ……………$\%$