The rate of disintegration of a fixed quantity of a radioactive element can be increased by

For a certain radioactive process,the graph between $\ln R$ and $t \, (\text{sec})$ is obtained as shown in the figure. Then the value of the half-life for the unknown radioactive material is approximately $.... \, \text{sec}$.

$A$ radioactive sample of half-life $ 10 $ days contains $ 1000x $ nuclei. The number of original nuclei present after $ 5 $ days is: (in $x$)

$A$ radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5\, minutes$,the rate becomes $1250$ disintegrations per minute. Then,its decay constant (per minute) is

The half-life period of a radioactive element $x$ is the same as the mean life time of another radioactive element $y$. Initially,they have the same number of atoms. Then:

$A$ radioactive sample consists of two distinct species having an equal number of $N_0$ atoms initially. The mean-life of one species is $\tau$ and of the other is $5\tau$. The decay products in both cases are stable. The total number of radioactive nuclei at $t = 5\tau$ is