The half-life of a radioactive substance is $40$ years. How long will it take to reduce to one fourth of its original amount and what is the value of decay constant

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

If a radioactive material remains $25 \%$ after $16$ days, then its half life will be ......... days

A radioactive material of half-life $T$ was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If now their present activities are $A_1$ and $A_2$ respectively then their age difference equals :

Two radioactive isotopes $P$ and $Q$ have half Jives $10$ minutes and $15$ minutes respectively. Freshly prepared samples of each isotope initially gontain the same number of atoms. After $30$ minutes, the ratio $\frac{\text { number of atoms of } P}{\text { number of atoms of } Q}$ will be

Radioacitive nuclei $A$ and $B$ disintegrate into $C$ with half lives $T$ and $2T$. At $t = 0$, pumber of nuclei of each $A$ and $B$ is $x$. The number of nuclei of $C$ when rate of disintegration of $A$ and $B$ are equal is