Activities of three radioactive substances $A , B$ and $C$ are represented by the curves $A, B$ and $C,$ in the figure. Then their half-lives $T _{\frac{1}{2}}( A ): T _{\frac{1}{2}}( B ): T _{\frac{1}{2}}( C )$ are in the ratio

$x$ fraction of a radioactive sample decay in $t$ time. How much fraction will decay in $2t$ time

A radioactive material decays by simultaneous emissions of two particles with half lives of $1400\, years$ and $700\, years$ respectively. What will be the time after which one third of the material remains? (Take In $3=1.1$ ) (In $years$)

The activity of a radioactive material is $6.4 \times 10^{-4}$ curie. Its half life is $5\; days$. The activity will become $5 \times 10^{-6}$ curie after $.......day$

Two radioactive elements $A$ and $B$ initially have same number of atoms. The half life of $A$ is same as the average life of $B$. If $\lambda_A$ and $\lambda_B$ are decay constants of $A$ and $B$ respectively, then choose the correct relation from the given options.

The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^9 s$. The mass of an atom of this radioisotope is $10^{-25} kg$. The mass (in $mg$ ) of the radioactive sample is