The half-life of a radioactive nuclide is

Two radioactive materials $M_1$ and $M_2$ have decay constants $9 \lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. The ratio of the number of nuclei of $M_1$ to that of $M_2$ will be $\frac{1}{e}$ after a time interval of:

An alloy is composed of two radioactive materials $A$ and $B$ having equal weight. The half-lives of $A$ and $B$ are $10 \ yrs$ and $20 \ yrs$ respectively. After time $t$,the alloy was found to consist of $(1/e) \ kg$ of $A$ and $1 \ kg$ of $B$. If the atomic weights of $A$ and $B$ are the same,then the value of $t$ is (Assume $\ln 2 = 0.7$):

If the half-life of a radioactive sample is $10\, hours$,its mean life is .......... $hours$.

In a sample of radioactive material,what fraction of the initial number of active nuclei will remain undisintegrated after half of a half-life of the sample?

$A$ and $B$ are two radioactive substances whose half-lives are $1$ and $2$ years respectively. Initially, $10 \, g$ of $A$ and $1 \, g$ of $B$ are taken. The time (approximate) after which they will have the same quantity remaining is ........... $years$.