If $A+B+C=270^{\circ}$,then $\cos 2A+\cos 2B+\cos 2C$ is equal to:

In $\triangle ABC$, the midpoints of the sides $AB, BC$, and $CA$ are respectively $(l, 0, 0), (0, m, 0)$, and $(0, 0, n)$. Then, $\frac{AB^2+BC^2+CA^2}{l^2+m^2+n^2}$ is equal to

The quadratic equations $x^2 - 6x + a = 0$ and $x^2 - cx + 6 = 0$ have one root in common. The other roots of the first and second equations are integers in the ratio $4 : 3$. Then the common root is

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium,the value of $q$ is:

Zener breakdown takes place if

If $f(2)=4$ and $f^{\prime}(2)=1$,then $\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}$ is equal to