$A$ certain radioactive substance reduces to $25\%$ of its initial value in $16$ days. Its half-life is ........ $days$.

If the line joining $A(1, 3, 4)$ and $B$ is divided by the point $P(-2, 3, 5)$ in the ratio $1: 3$, then the coordinates of $B$ are:

The steps of a plant breeding program are given below. Arrange them in the correct sequence.
$(a)$ Cross-hybridization among the selected parents
$(b)$ Testing,release,and commercialization of new cultivars
$(c)$ Collection of variability
$(d)$ Selection and testing of superior recombinants
$(e)$ Evaluation and selection of parents

Which one of the following removes temporary hardness of water?

In the Young's double slit experiment,the intensities at two points $P_1$ and $P_2$ on the screen are respectively $I_1$ and $I_2$. If $P_1$ is located at the centre of a bright fringe and $P_2$ is located at a distance equal to a quarter of fringe width from $P_1$,then $I_1/I_2$ is:

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is