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1.  
A room is 14 m long, 10 m wide and 5 m high. The cost of plastering its four walls at ₹ 30 per m² is:

Correct Answer: B [₹ 7,200]

Explanation:

Four walls = 2h(l + b) = 2 × 5 × 24 = 240 m² → 240 × 30 = ₹ 7,200.

2.  
The area of an equilateral triangle of side 12 cm is:

Correct Answer: C [36√3 cm²]

Explanation:

(√3/4) × 144 = 36√3 cm².

3.  
The length of a rectangle is increased by 25% and its breadth is decreased by 20%. The area:

Correct Answer: E [remains the same]

Explanation:

25 − 20 − 500/100 = 0% → no change.

4.  
The circumference of a circle is 88 cm. Its area is:

Correct Answer: A [616 cm²]

Explanation:

88 = 44 × 2 → r = 14 → area = 154 × 4 = 616 cm².

5.  
The area of a triangle with sides 10 cm, 17 cm and 21 cm is:

Correct Answer: D [84 cm²]

Explanation:

s = 24; √(24 × 14 × 7 × 3) = √7,056 = 84 cm².

6.  
A solid metal sphere of radius 9 cm is melted and recast into a cylinder of radius 6 cm. The height of the cylinder is:

Correct Answer: A [27 cm]

Explanation:

(4/3)π × 729 = π × 36 × h → h = 972/36 = 27 cm.

7.  
The length of the longest rod that can be placed in a box 12 cm × 4 cm × 3 cm is:

Correct Answer: D [13 cm]

Explanation:

Diagonal = √(144 + 16 + 9) = √169 = 13 cm.

8.  
A rectangular ground 50 m × 30 m has a path 3 m wide all round it on the outside. The area of the path is:

Correct Answer: E [516 m²]

Explanation:

2w(l + b + 2w) = 6 × 86 = 516 m².

9.  
Quantity I: Area (cm²) of a circle of radius 7 cm.
Quantity II: Area (cm²) of a square whose diagonal is 18 cm.

Correct Answer: B [Quantity I < Quantity II]

Explanation:

I: 154. II: d²/2 = 324/2 = 162.

10.  
What is the volume of the cylinder?
I. Its curved surface area is 880 cm².
II. Its radius is 7 cm.

Correct Answer: D [Both statements together are needed]

Explanation:

Need both: h = 880 ÷ 44 = 20 cm → V = 154 × 20 = 3,080 cm³.

11.  
Trick Spotter: the radius of a circle increases by 10%. Which gives the percentage change in its area fastest?

Correct Answer: B [2 × 10 + 10²/100 = 21%]

Explanation:

Area Merger for equal changes: 2r + r²/100 = 21%.

12.  
A cube has edge 5 cm. Which of the following is/are correct?
I. Its volume is 125 cm³.
II. Its total surface area is 150 cm².
III. Its diagonal is 5√2 cm.

Correct Answer: C [Only I and II]

Explanation:

a³ = 125 ✓; 6a² = 150 ✓; the cube's diagonal is a√3 = 5√3 (5√2 is a face diagonal) ✗.

13.  
The area of a sector of a circle of radius 21 cm with an angle of 60° is:

Correct Answer: C [231 cm²]

Explanation:

60/360 × 1,386 = 231 cm².

14.  
Reverse question: a cone of radius 7 cm has a volume of 1,232 cm³. What is its height?

Correct Answer: D [24 cm]

Explanation:

⅓ × 154 × h = 1,232 → h = 1,232 × 3/154 = 24 cm.

15.  
The area of an isosceles triangle whose equal sides are 17 cm each and whose base is 16 cm is:

Correct Answer: B [120 cm²]

Explanation:

Height = √(17² − 8²) = 15 (8–15–17) → area = ½ × 16 × 15 = 120 cm².

16.  
A cube of edge 15 cm is painted on all its faces and then cut into small cubes of edge 3 cm. How many small cubes have paint on exactly two faces?

Correct Answer: C [36]

Explanation:

n = 15/3 = 5 per edge → two faces painted = 12(n − 2) = 36.

17.  
The parallel sides of a trapezium are 18 cm and 12 cm and the distance between them is 8 cm. Its area is:

Correct Answer: D [120 cm²]

Explanation:

½ × (18 + 12) × 8 = 120 cm².

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