If a radioactive substance decays $10 \%$ in every $16 \text{ hours}$,then the percentage of the radioactive substance that remains after $2 \text{ days}$ is

$A$ radioactive substance contains $10000$ nuclei and its half-life period is $20$ days. The number of nuclei present at the end of $10$ days is

$A$ radioactive sample has a half-life of $3$ years. The time required for the activity of the sample to reduce to $\frac{1}{5}$th of its initial value is about (in $years$)

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 isotope $X$ has a half-life of $20$ years and decays into a stable element $Y$. In a given rock sample, the ratio of the amounts of $X$ and $Y$ is found to be $1:7$. The estimated age of the rock is ......... years.

At a given instant,a radioactive sample has $N$ active nuclei. If its decay constant is $\lambda$,which of the following relations is incorrect? (Note: $\lambda$ is very small.)