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 : The sides of similar triangle $\triangle ABC$ and $\triangle DEF$ are in the ratio of $\frac{\sqrt{3}}{\sqrt{5}}$. If the area of $\triangle ABC$ is $90 \text{ cm}^2$, then the area of $\triangle DFF\left(\right.$ in $\left.\text{cm}^2\right)$ is:

Option 1: 150

Option 2: 152

Option 3: 154

Option 4: 156

Question : ABCD is a square. Draw a triangle QBC on side BC considering BC as a base and draw a triangle PAC on AC as its base such that $\Delta$QBC$\sim\Delta$PAC. Then, $\frac{\text{Area of $\Delta$QBC}}{\text{Area of  $\Delta$PAC}}$ is equal to:

Option 1: $\frac{1}{2}$

Option 2: $\frac{2}{1}$

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

Option 4: $\frac{2}{3}$