In the adjoining figure, ∠ADE = ∠ABC, AE = 8 cm, EB = 7 cm, BC = 9 cm, AD = 10 cm and DC = 2 cm. Then the length of DE is:

1. 6 cm

2. 6.75 cm

3. 7.8 cm

4. 13.5 cm

In ΔABC, it is given that AB = 9 cm, BC = 6 cm and CA = 7.5 cm. Also ΔDEF is given such that EF = 8 cm and ΔDEF ∼ ΔABC. Then the perimeter of ΔDEF is:

1. 22.5 cm

2. 25 cm

3. 27 cm

4. 30 cm

In the given figure, two line segments AC and BD intersect each other at point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then ∠PBA = ?

1. 30°

2. 50°

3. 60°

4. 100°

ABCD is a trapezium with AB parallel to DC. Then the triangle similar to ΔAOB is:

1. ΔACB

2. ΔADB

3. ΔCOB

4. ΔCOD