$A$ radioactive sample has a half-life of $5 \text{ years}$. The percentage of the fraction decayed in $10 \text{ years}$ will be: (in $\%$)

The rate of disintegration of a radioactive sample is $R$ and the number of atoms present at any time $t$ is $N$. When $\frac{R}{N}$ is taken along the $Y$-axis and $t$ is taken along the $X$-axis,the correct graph is:

$A$ radio-isotope has a half-life of $5$ years. The fraction of the atoms of this material that would decay in $15$ years will be

The half-life of a neutron is $693 \ s$. What fraction of neutrons will decay when a beam of neutrons, having kinetic energy of $0.084 \ eV$, travels a distance of $1 \ km$? (mass of neutron $= 1.68 \times 10^{-27} \ kg$, and $\ln 2 = 0.693$)

$A$ 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?

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