If a radioactive element having half-life of $30\,min$ is undergoing beta decay, the fraction of radioactive element remains undecayed after $90\,min$. will be :

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.

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

The rate of disintegration of fixed quantity of a radioactive element can be increased by

Radioactivity was discovered by

A piece of wood from a recently cut tree shows $20\,decays$ per minute. A wooden piece of same size placed in a museum ( obtained from a tree cut many years back) shows $2\,decays$ per minute. If half life of $C^{14}$ is $5730\, years$, then age of the wooden piece placed in the museum is approximately ........... $years$