Mensuration, Basic Algebra, Basic Geometry - Question Bank

1. What is the diameter of a circle if its circumference is 88 cm? (Use π = 22/7)
A) 14 cm
B) 21 cm
C) 28 cm
D) 44 cm
2. If x:y = 2:3 and y:z = 4:5, what is x:z?
A) 2:5
B) 8:15
C) 3:5
D) 2:15
3. A rectangular prism has dimensions 4 cm, 5 cm, and 6 cm. What is its volume?
A) 15 cubic cm
B) 30 cubic cm
C) 60 cubic cm
D) 120 cubic cm
4. What is the sum of the angles in a quadrilateral?
A) 180 degrees
B) 270 degrees
C) 360 degrees
D) 540 degrees
5. If 4x - 5 = 2x + 7, what is the value of x?
A) 3
B) 4
C) 5
D) 6
6. A square is inscribed in a circle of radius 7 cm. What is the area of the square?
A) 49 sq cm
B) 98 sq cm
C) 147 sq cm
D) 196 sq cm
7. What is the value of (a+b)(a-b)?
A) a² + b²
B) a² - b²
C) a² + 2ab + b²
D) a² - 2ab + b²
8. If x/2 - x/3 = 4, what is the value of x?
A) 12
B) 18
C) 24
D) 36
9. What is the perimeter of a semicircle with radius r?
A) πr
B) 2πr
C) πr + 2r
D) 2πr + r
10. The area of a triangle is 54 sq cm. If its base is 12 cm, what is its height?
A) 6 cm
B) 9 cm
C) 12 cm
D) 18 cm
11. If x = 2, what is the value of (3x² + 2x - 1)?
A) 11
B) 15
C) 17
D) 21
12. A cone has a height of 12 cm and a slant height of 13 cm. What is its radius?
A) 3 cm
B) 4 cm
C) 5 cm
D) 6 cm
13. What is the measure of an exterior angle of an equilateral triangle?
A) 60 degrees
B) 90 degrees
C) 120 degrees
D) 180 degrees
14. The sum of two numbers is 50 and their difference is 10. What are the numbers?
A) 20 and 30
B) 25 and 25
C) 30 and 20
D) 35 and 15
15. If 3x + 2y = 15 and x - y = 5, what is the value of x?
A) 5
B) 6
C) 7
D) 8
16. What is the lateral surface area of a cylinder with radius r and height h?
A) πr²h
B) 2πrh
C) 2πr(r+h)
D) πr(r+h)
17. The area of a rhombus is 240 sq cm. If one of its diagonals is 20 cm, what is the length of the other diagonal?
A) 12 cm
B) 24 cm
C) 30 cm
D) 48 cm
18. In a right-angled triangle, the hypotenuse is 13 cm and one side is 5 cm. What is the length of the other side?
A) 8 cm
B) 10 cm
C) 12 cm
D) 15 cm
19. What is the value of √81 + √144?
A) 9
B) 12
C) 21
D) 25
20. If 2/3 of a number is 10, what is the number?
A) 15
B) 20
C) 25
D) 30
21. A rectangular garden is 15 meters long and 10 meters wide. It is surrounded by a path 2 meters wide. What is the area of the path?
A) 64 sq meters
B) 72 sq meters
C) 136 sq meters
D) 116 sq meters
22. If x² - 9 = 0, what are the possible values of x?
A) 3
B) -3
C) 3 and -3
D) 9
23. What is the volume of a sphere with radius 3 cm? (Use π = 22/7)
A) 264/7 cubic cm
B) 792/7 cubic cm
C) 132/7 cubic cm
D) 396/7 cubic cm
24. In a parallelogram ABCD, angle A = 75 degrees. What is the measure of angle B?
A) 75 degrees
B) 105 degrees
C) 115 degrees
D) 125 degrees
25. What is the area of a circle with diameter 14 cm? (Use π = 22/7)
A) 154 sq cm
B) 44 sq cm
C) 616 sq cm
D) 308 sq cm
26. The perimeter of a square is 36 cm. What is its area?
A) 81 sq cm
B) 36 sq cm
C) 18 sq cm
D) 9 sq cm
27. What is the value of a³ - b³ if a - b = 2 and ab = 3?
A) 10
B) 12
C) 14
D) 16
28. If 5(x - 2) = 3x + 4, what is the value of x?
A) 4
B) 7
C) 9
D) 11
29. A rectangular tank is 10m long, 5m wide, and 2m deep. What is its capacity in cubic meters?
A) 17 cubic meters
B) 100 cubic meters
C) 50 cubic meters
D) 20 cubic meters
30. What is the length of the diagonal of a square with side length 8 cm?
A) 8√2 cm
B) 16 cm
C) 8 cm
D) 16√2 cm
31. Two angles of a triangle are in the ratio 2:3, and the third angle is 60 degrees. Find the other two angles.
A) 40 degrees and 60 degrees
B) 48 degrees and 72 degrees
C) 50 degrees and 70 degrees
D) 60 degrees and 60 degrees
32. If x/3 + x/4 = 7, what is the value of x?
A) 10
B) 12
C) 14
D) 16
33. What is the total surface area of a cone with radius r and slant height l?
A) πrl
B) 2πr(r+l)
C) πr(r+l)
D) πr²l
34. The diagonals of a rhombus are 12 cm and 16 cm. What is its area?
A) 96 sq cm
B) 48 sq cm
C) 192 sq cm
D) 28 sq cm
35. A chord of a circle is equal to its radius. What is the angle subtended by the chord at the center?
A) 30 degrees
B) 45 degrees
C) 60 degrees
D) 90 degrees
36. What is the value of (x+y)² - (x-y)²?
A) 2xy
B) 4xy
C) x² + y²
D) x² - y²
37. If 2x + 3 = x + 8, what is the value of x?
A) 4
B) 5
C) 6
D) 7
38. A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π = 3.14)
A) 282.6 cubic cm
B) 94.2 cubic cm
C) 31.4 cubic cm
D) 188.4 cubic cm
39. What is the area of a parallelogram with base 12 cm and height 5 cm?
A) 30 sq cm
B) 60 sq cm
C) 17 sq cm
D) 24 sq cm
40. In a triangle ABC, if angle A = 60 degrees and angle B = 70 degrees, what is angle C?
A) 40 degrees
B) 50 degrees
C) 60 degrees
D) 70 degrees
41. What is the sum of the interior angles of a hexagon?
A) 540 degrees
B) 720 degrees
C) 900 degrees
D) 1080 degrees
42. If a² - b² = 20 and a - b = 4, what is the value of a + b?
A) 3
B) 5
C) 8
D) 10
43. What is the value of 2a + 3b if a = 4 and b = 2?
A) 14
B) 10
C) 12
D) 16
44. Solve for y: 3y - 7 = 14
A) 5
B) 6
C) 7
D) 8
45. If x + 5 = 10, what is the value of x?
A) 3
B) 5
C) 15
D) 2
46. A triangle has a base of 10 cm and a height of 8 cm. What is its area?
A) 40 sq cm
B) 80 sq cm
C) 50 sq cm
D) 100 sq cm
47. What is the volume of a cube with side length 5 cm?
A) 125 cubic cm
B) 150 cubic cm
C) 25 cubic cm
D) 75 cubic cm
48. If the length of a rectangle is twice its width, and its area is 72 square meters, what is its length?
A) 6 meters
B) 12 meters
C) 18 meters
D) 24 meters
49. A circle has a radius of 7 cm. What is its circumference? (Use π = 22/7)
A) 44 cm
B) 49 cm
C) 56 cm
D) 42 cm
50. The area of a square is 144 square centimeters. What is the length of its side?
A) 10 cm
B) 12 cm
C) 14 cm
D) 16 cm
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