Which of the following statements are true regarding radioactivity

$(I)$ All radioactive elements decay exponentially with time

$(II)$ Half life time of a radioactive element is time required for one half of the radioactive atoms to disintegrate

$(III)$ Age of earth can be determined with the help of radioactive dating

$(IV)$ Half life time of a radioactive element is $50\%$ of its average life periodSelect correct answer using the codes given belowCodes :

Give the equation form of exponential law. 

The half-life of a radioactive substance is $30$ minutes. The times (in minutes ) taken between $40\%$ decay and $85\%$ decay of the same radioactive substance is

Two radioactive materials $A$ and $B$ have decay constants $10\,\lambda $ and $\lambda $, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of $B$ will be $1/e$ after a time

A sample originally contaived $10^{20}$ radioactive atoms, which emit $\alpha -$ particles. The ratio of $\alpha -$ particles emitted in the third year to that emitted during the second year is $0.3.$ How many $\alpha -$ particles were emitted in the first year?