Carbon $ - 14$ decays with half-life of about $5,800\, years$. In a sample of bone, the ratio of carbon $ - 14$ to carbon $ - 12$ is found to be $\frac{1}{4}$ of what it is in free air. This bone may belong to a period about $x$ centuries ago, where $x$ is nearest to

$A$ and $B$ are two radioactive substances whose half lives are $1$ and $2$ years respectively. Initially $10\, gm$ of $A$ and $1\, gm$ of $B$ is taken. The time (approximate) after which they will have same quantity remaining is ........... $years$

The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute.$10$ minutes later, the rate becomes $2250$ disintegrations per minute. The approximate decay cons $.........\min^{-1}$

The radioactive sources $A$ and $B$ have half lives of $2\ hr$ and $4\ hr$  espectively, initially contain the same number of radioactive atoms. At the end of $2\  hours$, their rates of distintegration are in the ratio

A count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later the meter shows a count rate of $30$ per minute. The half-life of the source is ..........$min$

The radioactivity of a given sample of whisky due to tritium (half life $12.3$ years) was found to be only $3\%$ of that measured in a recently purchased bottle marked $"7$ years old". The sample must have been prepared about