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1.  
Two circles have the same centre and radii 21 cm and 14 cm. The area of the ring between them is:

Correct Answer: E [770 cm²]

Explanation:

π(R² − r²) = 22/7 × (441 − 196) = 22/7 × 245 = 770 cm².

2.  
How many coins of diameter 1.4 cm and thickness 0.2 cm must be melted to make a cylinder of diameter 7 cm and height 8 cm?

Correct Answer: B [1,000]

Explanation:

Ratio of volumes = (3.5² × 8)/(0.7² × 0.2) = 98/0.098 = 1,000.

3.  
The length of a rectangle is 3 m more than its breadth and its area is 270 m². Its perimeter is:

Correct Answer: A [66 m]

Explanation:

b(b + 3) = 270 → b = 15, l = 18 → perimeter = 66 m.

4.  
A wire bent into a square of side 22 cm is straightened and bent into a circle. The area of the circle is:

Correct Answer: D [616 cm²]

Explanation:

Wire = 88 cm = 2πr → r = 14 → area 616 cm².

5.  
Each edge of a cube is increased by 20%. The percentage increase in its total surface area is:

Correct Answer: A [44%]

Explanation:

Surface ∝ edge²: 1.2² = 1.44 → 44%.

6.  
A hemispherical bowl of internal radius 9 cm is full of oil. The oil is poured into cylindrical bottles of radius 1.5 cm and height 4 cm. How many bottles are filled?

Correct Answer: B [54]

Explanation:

Bowl = ⅔π × 729 = 486π; bottle = π × 2.25 × 4 = 9π → 54 bottles.

7.  
The curved surface area of a cylinder is 1,320 cm² and its volume is 9,240 cm³. Its height is:

Correct Answer: C [15 cm]

Explanation:

V/CSA = r/2 → r = 2 × 9,240/1,320 = 14 cm; h = 1,320 ÷ 88 = 15 cm.

8.  
Water flows at 3 m/s through a pipe of internal radius 10 cm into an empty tank 10 m × 8 m × 9.9 m. How long does it take to fill the tank?

Correct Answer: E [2 h 20 min]

Explanation:

Per hour: 22/7 × 0.01 × 3 × 3,600 = 2,376/7 m³; tank 792 m³ → 792 × 7/2,376 = 7/3 h = 2 h 20 min.

9.  
Eight spherical marbles of radius 3 cm are dropped into a cylindrical vessel of radius 12 cm partly filled with water. By how much does the water level rise?

Correct Answer: C [2 cm]

Explanation:

Rise = (8 × 4/3 × 27) ÷ 144 = 288 ÷ 144 = 2 cm (π cancels).

10.  
The diagonals of a rhombus are 16 cm and 30 cm. Its perimeter is:

Correct Answer: A [68 cm]

Explanation:

Half-diagonals 8 and 15 → side 17 (8–15–17) → 68 cm.

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