If the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ $(a \neq b)$ have a common root,then $a+b$ is equal to

The human hindbrain comprises three parts,one of which is:

Let $R$ be a reflexive relation on a finite set $A$ having $n$ elements,and let there be $m$ ordered pairs in $R$. Then

$A$ ray of light passes through four transparent media with refractive indices $\mu_1$,$\mu_2$,$\mu_3$,and $\mu_4$ as shown in the figure. The surfaces of all media are parallel. If the emergent ray $CD$ is parallel to the incident ray $AB$,we must have

Which among the following factors is the most important in making fluorine the strongest oxidising halogen?

What should be the angular speed of the earth,so that a body lying on the equator may appear weightless? $(g = 10\,m/s^2, R = 6400\,km)$