Three charges $Q$,$+q$,and $+q$ are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic potential energy of the configuration is zero if $Q$ is equal to

If in a right-angled triangle $ABC$,the hypotenuse $AB = p$,then $\overrightarrow{AB} \cdot \overrightarrow{AC} + \overrightarrow{BC} \cdot \overrightarrow{BA} + \overrightarrow{CA} \cdot \overrightarrow{CB}$ is equal to

For all real $x$,the minimum value of the function $f(x)=\frac{1-x+x^2}{1+x+x^2}$ is

$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \ mm$ at a certain temperature. The maximum temperature variation allowable during the ruling is .......... $^oC$ (Coefficient of linear expansion of steel $\alpha = 10 \times 10^{-6} \ K^{-1}$)

Which of the following is not a sex hormone?