In the figure,$X$ represents time and $Y$ represents the activity of a radioactive sample. Then the activity of the sample varies with time according to the curve:

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

The radioactivity of a certain radioactive element drops to $1/64$ of its initial value in $30 \, s$. Its half-life is ......... $s$.

The activity of a radioactive sample is measured as $9750$ counts per minute at $t = 0$ and as $975$ counts per minute at $t = 5$ minutes. The decay constant is approximately ............ per minute.

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at time $t_2$. If $\lambda$ is the decay constant,then which of the following is correct?

The mean lives of a radioactive sample are $30 \, years$ and $60 \, years$ for $\alpha$-emission and $\beta$-emission,respectively. If the sample decays by both $\alpha$-emission and $\beta$-emission simultaneously,then the time after which only one-fourth of the sample remains is approximately ............ $years$.