The half-life of a radioactive substance is $5$ years. After $x$ years,a given sample of the radioactive substance gets reduced to $6.25 \%$ of its initial value. The value of $x$ is ...............

The mean life of a radioactive material for alpha decay and beta decay are,respectively,$1620$ years and $520$ years. What is the half life of the sample (in years)?

The graph represents the decay of a newly prepared sample of radioactive nuclide $X$ to a stable nuclide $Y$. The half-life of $X$ is $t$. The growth curve for $Y$ intersects the decay curve for $X$ after time $T$. What is the time $T$?

$A$ radioactive substance decays by $10\%$ in $5$ days. What percentage of the original substance will remain after $20$ days (in $\%$)?

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