Question : If in a $\triangle$PQR, $\angle$P = $88^\circ$, PQ and PR are produced to points S and T respectively. If the bisectors of $\angle$SQR and $\angle$TRQ meet at the point O. Find $\angle$QOR.

Option 1: $42^\circ$

Option 2: $46^\circ$

Option 3: $44^\circ$

Option 4: $48^\circ$

Question : $\triangle P Q R$ is similar to $\triangle \mathrm{UVW}$. Perimeters of $\triangle \mathrm{PQR}$ and $\Delta \mathrm{UVW}$ are 120 cm and 240 cm respectively. If PQ = 30 cm, then what is the length of UV?

Option 1: 45 cm

Option 2: 75 cm

Option 3: 60 cm

Option 4: 90 cm

Question : Two circles touch each other externally at any point C. PQ is the direct common tangent to both the circles touching the circles at point P and point Q. If the radii of the circles are 36 cm and 16 cm, respectively, then the length of PQ is:

Option 1: 42 cm

Option 2: 24 cm

Option 3: 48 cm

Option 4: 36 cm

Question : The perimeters of two similar triangles $\triangle$ABC and $\triangle$PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then AB is:

Option 1: 15 cm

Option 2: 12 cm

Option 3: 14 cm

Option 4: 26 cm

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