$10 \, g$ of radioactive material of half-life $15 \, \text{years}$ is kept in store for $20 \, \text{years}$. The disintegrated material is ............ $g$.

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to those of $B$ will be $(1/e)^2$ after a time interval of:

$x$ fraction of a radioactive sample decays in $t$ time. What fraction will decay in $2t$ time?

The graph in the figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t$. The relationship between $A$ and $t$ is (Assume $\ln 12 = 2.6$):

$A$ radioactive substance decays to $1/64$ of its initial value in $15$ hours. Find its half-life in hours.

$A$ radioactive sample decays at a rate of $5000$ disintegrations/minute at a certain instant. After $5$ minutes, the rate becomes $1250$ disintegrations/minute. The decay constant is ....... (in $\ln 2$)