If $3/4$ of a radioactive sample decays in $3/4 \, s$,then the half-life of the sample is ........ .

Two radioactive substances $X$ and $Y$ initially contain equal number of nuclei. $X$ has a half-life of $1\, hour$ and $Y$ has a half-life of $2\, hours$. After $2\, hours$,the ratio of the activity of $X$ to the activity of $Y$ is

The graph in the figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t$. The relationship between $A$ and $t$ is (Assume $\ln 12 = 2.6$):

The activity of a radioactive substance can be represented by various units. Select the correct option.

The half-life of ${ }_{84}^{209} Po$ is $103 \text{ years}$. The time it takes for a $100 \text{ g}$ sample of ${ }_{84}^{209} Po$ to decay to $3.125 \text{ g}$ is

An element $X$ with a half-life of $1.4 \times 10^9$ years decays to form another stable element $Y$. $A$ sample is taken from a rock that contains both $X$ and $Y$ in the ratio $1:7$. If at the time of formation of the rock,$Y$ was not present in the sample,then the age of the rock in years is