$1\, Curie $ is equal to

A radioactive nucleus ${ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X}$ undergoes spontaneous decay in the sequence

${ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \rightarrow {}_{\mathrm{Z}-1}{\mathrm{B}} \rightarrow {}_{\mathrm{Z}-3 }\mathrm{C} \rightarrow {}_{\mathrm{Z}-2} \mathrm{D}$, where $\mathrm{Z}$ is the atomic number of element $X.$ The possible decay particles in the sequence are :

If half life of radium is $77$ days. Its decay constant in day will be

Half-life is measured by

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