The areas of two similar triangles are 81 cm² and 144 cm². If the largest side of the smaller triangle is 27 cm, then largest side of the larger triangle is:

1. 24 cm

2. 36 cm

3. 48 cm

4. none of these

ΔABC and ΔDEF are similar to each other. If the ratio of side AB to side DE is $(\sqrt{2} + 1) : \sqrt{3}$, then the ratio of area of ΔABC to that of ΔDEF is:

1. $(3 + 2\sqrt{2}) : 3$

2. $1 : (9 - 6\sqrt{2})$

3. $(9 - 6\sqrt{2}) : 2$

4. $(3 - 2\sqrt{2}) : 3$

In the given figure, ∠CAB = 90° and AD ⟂ BC. If AC = 75 cm, AB = 1 m and BC = 1.25 m, then AD equals:

1. 50 cm

2. 60 cm

3. 65 cm

4. 70 cm

A street lamp is fixed on a lamp-post at a height of 3.3 m from the ground. A boy 110 cm tall walks away from the base of this lamp post at a speed of 0.8 m/s. The length of the shadow of the boy after 4 seconds is:

1. 1.1 m

2. 1.6 m

3. 2.1 m

4. 2.6 m