If a radioactive element having half-life of $30\,min$ is undergoing beta decay, the fraction of radioactive element remains undecayed after $90\,min$. will be :

The rate of disintegration was observed to be ${10^{17}}$ disintegrations per sec when its half life period is $1445$ years. The original number of particles are

After five half lives what will be the fraction of initial substance

The count rate for $10\  g$ of radioactive material was measured at different times and this has been shown in the graph with scale given. The half life of the material and the total count in the first half value period respectively are

Half lives of two radioactive nuclei $A$ and $B$ are $10\, minutes$ and $20\, minutes$, respectively. If, initially a sample has equal number of nuclei, then after $60$ $minutes$ , the ratio of decayed numbers of nuclei $A$ and $B$ will be

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 ...... minute