Radioactivity Questions

The half-life of a radioactive isotope $X$ is $50\text{years}$. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1:15$ in a sample of a given rock. The age of the rock was estimated to be:

A nucleus ${}_n^{m}X$ emits one $\alpha$ particle and two $\beta$ -particles. The resulting nucleus is:

A radioactive material has a half-life of $10\text{days}$. What fraction of the material would remain after $30\text{days}$?

In radioactive decay process, the negatively charged emitted $\beta$ -particles are:

Two radioactive substances $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t=0$ they have the same number of nuclei. The ratio of the number of nuclei of $A$ to those of $B$ will be $1/e^2$ after a time interval:

Two radioactive materials $X_1$ and $X_2$ have decay constants $5\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $1/e$ after a time:

In the nuclear decay given below:
$${}_Z^{A}X\stackrel{1}{\to }{}_{Z+1}^{A}Y\stackrel{2}{\to }{}_{Z-1}^{A-4}{B}^{\ast }\stackrel{3}{\to }{}_{Z-1}^{A-4}B$$
The particles emitted in the sequence are:

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:

The activity of a radioactive sample is measured as $N_0\text{ counts per minute}$ at $t=0$ and $N_0/e\text{ counts per minute}$ at $t=5\text{ minutes}$. The time (in minutes) at which the activity reduces to half its value is:

Two nuclei $P$ ($4N_0,T_{1/2}=1\text{m}$) and $Q$ ($N_0,T_{1/2}=2\text{m}$) decay to $R$. When $P=Q$, the number of $R$ nuclei present is:

Half life is $50$ days. Time interval $(t_2-t_1)$ between when $2/3$ has decayed and $1/3$ has decayed is:

A mixture consists of two radioactive materials $A_1$ and $A_2$ with half-lives of $20\text{s}$ and $10\text{s}$ respectively. Initially the mixture has $40\text{g}$ of $A_1$ and $160\text{g}$ of $A_2$. The amount of the two in the mixture will become equal after:

The half-life of a radioactive isotope 'X' is $20\text{years}$. It decays to stable element 'Y'. The ratio of 'X' to 'Y' in a rock is $1:7$. The age of the rock is:

A radio isotope 'X' with a half life $1.4\times 10^9\text{years}$ decays to 'Y' which is stable. A sample of the rock from a cave was found to contain 'X' and 'Y' in the ratio $1:7$. The age of the rock is:

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:

The half-life of a radioactive substance is $30\text{minutes}$. The time (in minutes) taken between $40\%$ decay and $85\%$ decay of the same radioactive substance is: