Question : In triangle STU, V is a point on the side ST and W is a point on the side SU such that VWUT is a trapezium. Given that VW : TU = 2 : 7, what is the ratio of the area of trapezium VWUT to the area of the triangle STU?

Option 1: 4 : 49

Option 2: 4 : 45

Option 3: 45 : 49

Option 4: 49 : 81

Question : $\triangle \mathrm{MNO}$ is similar to $\triangle \mathrm{STU}$. Perimeters of $\triangle \mathrm{MNO}$ and $\triangle \mathrm{STU}$ are 80 cm and 200 cm respectively. If ON = 25 cm, then what is the length of TU?

Option 1: 59 cm

Option 2: 61 cm

Option 3: 62.5 cm

Option 4: 60.5 cm

Question : In $\triangle \mathrm{STU}, \mathrm{SX}$ is the median on $\mathrm{TU}$. If $\mathrm{SX}=\mathrm{TX}$, then what is the value of $\angle \mathrm{TSU}$?

Option 1: 75°

Option 2: 45°

Option 3: 60°

Option 4: 90°

Question : Simplify the expression: $\frac{(u–v)^{3}+(v–w)^{3}+(w–u)^{3}}{(u^{2}–v^{2})^{3}+(v^{2}–w^{2})^{3}+(w^{2}–u^{2})^{3}}$

Option 1: $\frac{1}{(u+v)(v+w)(w+u)}$

Option 2: $1$

Option 3: $\frac{3}{(u+v)(v+w)(w+u)}$

Option 4: $0$

Question : Directions: In a certain code language,
W + V means W is the sister of V;
W # V means W is the husband of V;
W \$ V means W is the daughter of V;
W % V means W is the mother of V;
W @ V means W is the brother of V.
Based on the above, which of the following expressions denotes that Y is the wife of Z?

Option 1: Z @ R + K + P % Y

Option 2: P \$ Y % R + K % Z

Option 3: Y % P # K + R % Z

Option 4: Y % P + K @ R \$ Z

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: $21:4$