$A$ 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

If the undecayed fraction of a radioactive sample is $7/8$ after $6$ days,what will be the undecayed fraction after $10$ days?

Half-life of a radioactive sample is $24 \,h$. If a newly prepared radioactive sample shows $4$ times the allowed and safe value of radioactivity, the minimum time after which one can work safely with the source is (in $\,h$)

The atomic weight of a radioactive element is $M_w$ grams. The radioactivity of $m$ grams of this element is ......... ($N_A$ is Avogadro's number,$\lambda$ is the decay constant).

$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620$ years and $810$ years. The time (in years) after which one-fourth of the material remains is:

$A$ radioactive substance decays to $\left(\frac{1}{16}\right)^{th}$ of its initial activity in $80\, days$. The half-life of the radioactive substance expressed in days is ... .