Q.1. The length of the longest rod which can fit into a cubical room of 5 m side is

A. 5.334 m

B. 12.11 m

C. 9.320 m

D. 8.440 m

E. 3.050 m

Sol : Option B
Length of longest rod, which can fit into cubical room, is √3 × side.
Hence the answer is √3 × 7 = 12.11m

Q.2. The breadth of a garden is half its length. A playground measuring 45 sq. metre occupies one fourth of the total area of the garden. The length of the garden is

A. 6m

B. 3m

C. 4m

D. 5m

E. 2m

Sol : Option A L = 2B. Total area of the garden = 45 × 4 = 180 sq m. ∴ LB = 180 ⇒ L = 6m

Q.3. The diagonals of a rhombus are 4m and 3m. What is the length of each side of the rhombus?

A. 2.5m

B. 3.5m

C. 4.5m

D. 5.5m

E. 6.5m

Sol : Option A
Diagonals are 4 cm and 3 m
&there4 half of the diagonals is 2m and 1.5m.
∴ Side of rhombus is √1.5^{2} + 2^{2} = √2.25+4 = √6.25 = 2.5m

Q.4. One side of a rhombus is 10 cm. If the length of one of its diagonals is 16 cm, then the length of the other diagonal is

A. 2cm

B. 16cm

C. 18cm

D. 20cm

E. 12cm

Sol : Option E
Side of rhombus = 10 cm.
Half of the diagonal = 16 / 2 = 8 cm
∴ half of the other diagonal = ×10^{2} - 8^{2} = √ 2.25 + 4 = √6.25 = 2.5m
∴ length of other diagonal = 6 × 2
= 12 cm

Q.5. The measure of an angle which is five times its complement is

A. 26°

B. 75°

C. 78°

D. 18°

E. 122°

Sol : Option B
Let the angle be x.
∴ x = 5(90 – x)
⇒ x = 450 – 5x
⇒ 6x = 450 ⇒ x = 750

Q.6. The base of a prism is a triangle of sides 6, 8 and 10 m respectively. The height of the prism is 20 m. Find its volume.

A. 240 m^{3}

B. 480 m^{3}

C. 420 m^{3}

D. 315 m^{3}

E. 150 m^{3}

Sol : Option B
Volume of prism = Base Area ⇒ Height. Base area = √s(s-a)(s-b)(s-c) where s = (6+8+10)/2 = 12 Base area = √ 12× 6× 4 ×2 = 24m^{2} ∴ Volume of prism = 24×20 = 480m^{3}

Q.7. If the breadth of a rectangle is decreased by 20 % and the length increased by 10 %, a square of area 1936 m2 is obtained. The area of the rectangle in square metres is

A. 2200

B. 3500

C. 2250

D. 1450

E. 4506

Sol : Option A
1.1L × 0.8B = 1936 ⇒ LB = 2200m^{2}.
∴ Area of rectangle = 2200m^{2}.

Q8. What is the arc length that is intercepted by an inscribed angle of 42o on a circle with radius 24?

A. 70.4

B. 325.2

C. 324

D. 7.6

E. 233.2

Sol : Option B
Angle on a circle is half of the angle at the center.
∴ angle = 84.
Length of the arc = 2πr(θ/360) = 2 × (22/7) × 24 × 24 × 84/360 =70.4

Q9. The height of a cylinder is 16 cm and the radius of the base is 6 cm. Find the area of the curved surface of the cylinder.

A. 480 sqcm

B. 560 sqcm

C. 603 sqcm

D. 720 sqcm0

E. 800 sqcm

Sol : Option C
The surface area = 2 πrh
= 2 π×6×16
= 603 sq.cm

Q10. A swimming bath is 240 m long and 12.5 m wide. How many litres must be pumped into it to raise the water-level by 1 cm?

A. 3,000 litres

B. 300,000 litres

C. 30,000 litres

D. 3,000,000 litres

E. 300 litres

Sol : Option B
Required volume of water
= 240 × 12.5 × 0.01
= 30 cu.m.
1 m^{3} = 1000 litre.
30 cu m = 30 × 1000
= 300,00 litres