At time $t = 0$,a radioactive element has a mass of $10 \, gm$. What mass in $gm$ will remain after two mean lifetimes?

The half-life period of a radioactive element $A$ is $62 \text{ years}$. It decays into another stable element $B$. An archaeologist found a sample in which $A$ and $B$ are in $1 : 15$ ratio. The age of the sample is (in $\text{ years}$)

In the radioactive decay of an element,it is found that the count rate reduces from $1024$ to $128$ in $3$ minutes. Its half-life will be ...... minutes.

The average life $T$ and the decay constant $\lambda$ of a radioactive nucleus are related as

$A$ radioactive material decays by simultaneous emissions of two particles with half-lives of $1400 \, years$ and $700 \, years$ respectively. What will be the time after which one-third of the material remains? (Take $\ln 3 = 1.1$) (In $years$)

$A$ radioactive sample consists of two distinct species having an equal number of atoms initially. The mean life time of one species is $\tau$ and that of the other is $5 \tau$. The decay products in both cases are stable. $A$ plot is made of the total number of radioactive nuclei as a function of time. Which of the following figures best represents the form of this plot?