1. ABC is a right angled triangle, B being the right angle. Mid-points of BC and AC are respectively B’ and A’. The ratio of the area of the quadrilateral AA’B’B of the area of the triangle ABC is

(a) 1 : 2

(b) 2 : 3

(c) 3 : 4

(d) None of the above

Solution :

2.A cuboidal water tank has 216 litres of water. Its depth is 1/3 of its length and breadth is 1/2 of 1/3 of the difference of length and height. The length of the tank is

(a) 72 dm

(b) 18 dm

(c) 6 dm

(d) 2 dm

Ans.(b)

Sol. Let l=9x, h=3x, b=x

l×b×h=216×1000

(1 litre = 1000 cm3)

9x×3x×x=216000

27x³=216000

x³=8000

x=20

l=180 cm = 18 dm

3. A wooden box measures 20 cm by 12 cm by 10 cm. Thickness of wood is 1 cm. Volume of wood to make the box (in cube cm) is

(a) 960

(b) 519

(c) 2400

(d) 1120

Ans.(a)

Sol. The external dimensions of the box are

l = 20 cm, b = 12 cm, h = 10 cm

External volume of the box = 20 × 12 × 10 = 2400 cm3

Thickness of the wood = 1 cm

Internal length = 20 – 2 = 18 cm

Internal breadth = 12 – 2 = 10 cm

Internal height = 10 – 2 = 8 cm

Internal volume of the box = 18 × 10 × 8 = 1440 cm3

Volume of the wood = (2400 – 1440) cm3

= 960 cm3

4. Two circles with centres A and B and radius 2 units touch each other externally at ‘C’ A third circle with centre ‘C’ and diameter ‘4’ units meets other two at D and E. Then the area of the quadrilateral ABED is

(a) 2√2 sq. units

(b) 3√3 sq. units

(c) 3√2 sq. units

(d) 2√3 sq. units

Answer :