If $a^x = b$,$b^y = c$,and $c^z = a$,then the value of $xyz$ is:

Half-life of a radioactive substance is $20 \ minutes$. The time between $20\%$ and $80\%$ decay will be ........... $minutes$.

Which property among the following is the same for both hydrogen and deuterium molecules?

$4 \tan^{-1} \frac{1}{5} - \tan^{-1} \frac{1}{239}$ is equal to

The area (in sq unit) of the region bounded by the curves $2x = y^2 - 1$ and $x = 0$ is

$A$ tank with vertical walls is mounted so that its base is at a height $H$ above the horizontal ground. The tank is filled with water to a depth $h$. $A$ hole is punched in the side wall of the tank at a depth $x$ below the water surface. To have maximum range of the emerging stream, the value of $x$ is