Question : D and E are points on sides AB and AC of $\Delta ABC$. DE is parallel to BC. If AD : DB = 2 : 3. What is the ratio of the area of $\Delta ADE$ and the area of quadrilateral BDEC?

Option 1: 4 : 21

Option 2: 4 : 25

Option 3: 4 : 29

Option 4: 4 : 9

Question : In $\triangle ABC$ and $\triangle PQR, \angle B=\angle Q, \angle C=\angle R$ and $AB=2PQ$, then the two triangles are:

Option 1: congruent as well as similar

Option 2: neither similar nor congruent

Option 3: similar but not congruent

Option 4: congruent but not similar

Question : In $\triangle ABC$, $D$ and $E$ are the points of sides $AB$ and $BC$ respectively such that $DE \parallel AC$ and $AD : DB = 3 : 2$. The ratio of the area of trapezium $ACED$ to that of $\triangle DBE$ is:

Option 1: $4:15$

Option 2: $15:4$

Option 3: $4:21$

Option 4: $21:4$

Question : In $\Delta ABC$ the straight line parallel to the side $BC$ meets $AB$ and $AC$ at the point $P$ and $Q,$ respectively. If $AP=QC$, the length of $AB$ is $\operatorname{12 units}$ and the length of $AQ$ is $\operatorname{2 units}$, then the length (in units) of $CQ$ is:

Option 1: $4$

Option 2: $6$

Option 3: $8$

Option 4: $10$

Question : In $\triangle$ABC, D and E are two points on the sides AB and AC, respectively, so that DE $\parallel$ BC and $\frac{AD}{BD}=\frac{2}{3}$. Then $\frac{\text{Area of trapezium DECB}}{\text{Area of $\triangle$ABC}}$ is equal to:

Option 1: $\frac{5}{9}$

Option 2: $\frac{21}{25}$

Option 3: $1\frac{4}{5}$

Option 4: $5\frac{1}{4}$