If the half-life of a radioactive element is $3 \ hours$,what fraction of its initial activity remains after $9 \ hours$?

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at a later time $t_2$. Its decay constant is $\lambda$. Which of the following relations is correct?

Activity of a radioactive sample decreases to $(1/4)^{th}$ of its original value in $4 \text{ days}$. Then in $16 \text{ days}$ its activity will become $x$ times the original value. The value of $x$ is

Half-life of a radioactive element is $10 \, days$. The time during which the quantity remains $1/10$ of the initial mass will be ......... $days$.

$A$ 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 ........... $years$.

Two radioactive materials $A$ and $B$ have decay constants $10\lambda$ and $\lambda$,respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $A$ to that of $B$ will be $1/e$ after a time: