ABC is a triangle, the point P is on side BC such that $3\bar{BP}=2\bar{PC}$, the point Q is on the line $\bar{CA}$ such that $4\bar{CQ}=\bar{QA}$. If R is the common point $\bar{AP}$ & $\bar{BQ}$, then the ratio in which the fine joining CR divides $\bar{AB}$ is?

If a straight line $y-x=2$ divides the region ${x}^{2}+{y}^{2}\le 4$ into two parts, then the ratio of the area of the smaller part to the area of the greater part is 

The line joining points $(3,5)$ and $(2,7)$ is divided by $X-$ axis in the ratio.

The point $(\dfrac{7}{4},\dfrac{7}{8})$ divides the line segment joining the points (4,-1) and (-2,4) internally in the ratio 3 : 5.

The ratio in which the point (4, 7) divides the line segment joining (1, 4) and (11, 14) is 

A square sheet of paper $ABCD$ is so folded that $B$ falls on the mid point $M$ of $CD$. The crease will divide $BC$ in the ratio :

$42,000$ millimeters long wire is cut equally at $6$ places. Find the length of each piece of wire.

Perpendicular from the origin to the line joining the points $(c \, cos \alpha, c \, sin \alpha)$ and $(c \, cos \beta , \, c \, sin \beta)$ divides it in the ratio

The join of $(4, 5)$ and $(1,2)$ is divided by y-axis in the ratio 

The point which divides the line segment joining $(-2, 4), (2, 7)$ in the ratio $2:1$ externally is

Find the points $A(a, b), B(-a, -b)$ and $P(a^2, ab)$ are collinear then the ratio in which p divides $\overline{AB}$ is 

The plane XOZ divides the join of (1, -1, 5) and (2, 3, 4) in the ratio $\lambda : 1$, then $\lambda$ is 

In $\triangle ABC$ $PQR$ $\overline { BC } .\overline { CA } .\overline { AB } $ respectively dividing them in the ratio $1:4,3:2$ and $3:7$. The point $S$ divides $AB$ in the ratio $1:3$ Then $\dfrac { \left| \overline { AP } +\overline { BQ } +\overline { CR }  \right|  }{ \left| CS \right|  } =$

A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at point P and Q respectively. Then the point O divides the segment PQ in the ratio

The ratio in which the line segment joining the points $\left(3,-4\right)$ and $\left(-5,6\right)$ is divided by the $x-$ axis, is

The ratio in which the point $(x _{1} \sin^{2} \theta, y _{1} \cos^{2} \theta)$ divides the line joining $(x _{1}, 0)$ and $(0, y _{1})$ is -

A point which divides the joint of $(1,2)$ and $(3,4)$ externally in the ratio $1:1$

If the ratio in which the line segment joining the points (6,4) and (x,-7) divided internally by y-axis is 6: 1, then x equals