If the line $2x - y - 4 = 0$ divides the line segment joining the points $(2, -1)$ and $(1, -4)$ at the point $(a, b)$ in the ratio $m:n$,then $4(a - b(\frac{m}{n})^2) = $

Let $O(0, 0)$, $A(-1, 2)$ and $B(1, 3)$ be the vertices of $\Delta OAB$. The bisector of $\angle O$ intersects side $AB$ at point $D$. The value of $OD \cdot AB$ is equal to...

If the portion of a straight line intercepted between the coordinate axes is divided by the point $(2,3)$ in the ratio $2:3$,then the product of the intercepts made by this line on the axes is

The point $A$ divides the join of the points $(-5, 1)$ and $(3, 5)$ in the ratio $k : 1$. The coordinates of the points $B$ and $C$ are $(1, 5)$ and $(7, -2)$ respectively. If the area of the triangle $ABC$ is $2$ square units,then $k =$

Points $Q, R,$ and $S$ lie on the line segment joining $P(a, x)$ and $T(b, y)$ such that $PQ = QR = RS = ST$. If $L\left( \frac{5a + 3b}{8}, \frac{5x + 3y}{8} \right)$ is a point on the segment,then $L$ is the midpoint of which line segment?

The inclination of the straight line passing through the point $(-3, 6)$ and the midpoint of the line joining the points $(4, -5)$ and $(-2, 9)$ is