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 : If in a $\triangle$ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and $\frac{AD}{BD}$ = $\frac{3}{5}$. If AC = 4 cm, then AE is:

Option 1: 1.5 cm

Option 2: 2.0 cm

Option 3: 1.8 cm

Option 4: 2.4 cm

Question : In triangle RST, M and N are two points on RS and RT such that MN is parallel to the base ST of the triangle RST. If $\text{RM}=\frac{1}{3} \text{MS}$ and $\text{ST}=5.6 \text{ cm}$, what is the ratio of $\frac{\text { Area of triangle RMN}}{\text {Area of trapezium MNST}}$?

Option 1: $\frac{14}{15}$

Option 2: $\frac{15}{16}$

Option 3: $\frac{1}{15}$

Option 4: $\frac{1}{16}$

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 a $\triangle ABC$, the median AD, BE, and CF meet at G, then which of the following is true?

Option 1: 4(AD + BE + CF) > 3(AB + BC + AC)

Option 2: 2(AD + BE + CF) > (AB + BC + AC)

Option 3: 3(AD + BE + CF) > 4(AB + BC + AC)

Option 4: AB + BC + AC > AD + BE + CF