Question : Point A divides segment BC in the ratio 4 : 1. Coordinates of B are (6, 1) and coordinates of C are ($\frac{7}{2}$, $6$). What are the coordinates of point A?

Question : The graphs of the equations
$4 x+\frac{1}{3} y=\frac{8}{3}$ and $\frac{1}{2} x+\frac{3}{4} y+\frac{5}{2}=0$ intersect at a point P. The point P also lies on the graph of the equation:

Question : If $a+b+c = 0$, then the value of $\small \frac{1}{(a+b)(b+c)}+\frac{1}{(b+c)(c+a)}+\frac{1}{(c+a)(a+b)}$ is:

Question : Super cooling stands for cooling of a liquid:

Question : If $a+b+c=0$, the value of $\frac{a^2+b^2+c^2}{a^2-bc}$ is: