$A$ radioactive element has a half-life of $15$ years. What is the fraction that will decay in $30$ years?

The fraction $f$ of radioactive material that has decayed in time $t$,varies with time $t$. The correct variation is given by the curve

The half-life of a radioactive element depends upon:

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.)

The half-life period of a radioactive element $X$ is the same as the mean life time of another radioactive element $Y$. Initially,both of them have the same number of atoms. Then:

Activity of a radioactive sample decreases to $(1/4)^{th}$ of its original value in $4 \text{ days}$. Then in $16 \text{ days}$ its activity will become $x$ times the original value. The value of $x$ is