Mensuration, Geometry and Trigonometry - Question Bank

1. What is the value of sin(30°) * cos(60°)?
A) 1/4
B) 1/2
C) 1
D) 0
2. If the area of an equilateral triangle is 4√3 sq. cm, what is its side length?
A) 4 cm
B) 2 cm
C) 8 cm
D) 16 cm
3. A cylinder has a radius of 5 cm and a height of 10 cm. What is its total surface area?
A) 150π sq. cm
B) 50π sq. cm
C) 100π sq. cm
D) 200π sq. cm
4. What is the value of (tan(45°) + sin(30°)) / cos(60°)?
A) 3
B) 1.5
C) 2
D) 0.5
5. A circle is inscribed in a square of side 14 cm. What is the area of the circle?
A) 154 sq. cm
B) 49 sq. cm
C) 196 sq. cm
D) 98 sq. cm
6. The sum of the angles in a quadrilateral is:
A) 360°
B) 180°
C) 540°
D) 720°
7. What is the value of cosec(30°)?
A) 2
B) 1/2
C) √3
D) 1/√3
8. If sin(θ) = cos(θ), what is the value of θ in degrees?
A) 45°
B) 30°
C) 60°
D) 90°
9. The area of a trapezoid is 100 sq. cm. If its height is 10 cm and one parallel side is 8 cm, what is the other parallel side?
A) 12 cm
B) 10 cm
C) 20 cm
D) 16 cm
10. What is the value of cot(30°)?
A) √3
B) 1/√3
C) 1
D) 2
11. A right-angled triangle has angles 30°, 60°, and 90°. If the side opposite to 30° is 5 cm, what is the hypotenuse?
A) 10 cm
B) 5√3 cm
C) 15 cm
D) 5 cm
12. The perimeter of a rectangle is 50 cm. If its length is 15 cm, what is its breadth?
A) 10 cm
B) 20 cm
C) 5 cm
D) 25 cm
13. What is the value of sin(0°) + cos(90°)?
A) 0
B) 1
C) 2
D) -1
14. If tan(θ) = 1/√3, what is the value of θ in degrees?
A) 30°
B) 60°
C) 45°
D) 90°
15. A regular hexagon has a side length of 10 cm. What is its area?
A) 150√3 sq. cm
B) 75√3 sq. cm
C) 300√3 sq. cm
D) 50√3 sq. cm
16. The radius of a hemisphere is 6 cm. What is its volume?
A) 144π cubic cm
B) 72π cubic cm
C) 288π cubic cm
D) 36π cubic cm
17. What is the value of sec(60°)?
A) 2
B) 1/2
C) √3
D) 1/√3
18. If sin(θ) = 1/2, what is the value of θ in degrees?
A) 30°
B) 60°
C) 45°
D) 90°
19. A triangle has base 10 cm and height 7 cm. What is its area?
A) 35 sq. cm
B) 17 sq. cm
C) 70 sq. cm
D) 100 sq. cm
20. What is the lateral surface area of a cube with side length 4 cm?
A) 64 sq. cm
B) 96 sq. cm
C) 16 sq. cm
D) 32 sq. cm
21. If tan(θ) = √3, what is the value of θ in degrees?
A) 60°
B) 30°
C) 45°
D) 90°
22. A sector of a circle has a radius of 7 cm and an angle of 60°. What is its area?
A) 154/6 sq. cm
B) 49/6 sq. cm
C) 154 sq. cm
D) 49 sq. cm
23. What is the value of sin(90°) + cos(0°)?
A) 2
B) 1
C) 0
D) 0.5
24. If cos(θ) = 0, what is the value of θ in degrees?
A) 90°
B) 0°
C) 180°
D) 270°
25. A rhombus has diagonals of length 12 cm and 10 cm. What is its area?
A) 60 sq. cm
B) 22 sq. cm
C) 120 sq. cm
D) 30 sq. cm
26. What is the volume of a cylinder with radius 2 cm and height 7 cm?
A) 28π cubic cm
B) 14π cubic cm
C) 4π cubic cm
D) 49π cubic cm
27. In a triangle ABC, angle B = 90°. If AB = 5 cm and BC = 12 cm, what is AC?
A) 13 cm
B) 17 cm
C) 10 cm
D) 25 cm
28. The diameter of a circle is 14 cm. What is its area?
A) 154 sq. cm
B) 44 sq. cm
C) 196 sq. cm
D) 28 sq. cm
29. A cone has a radius of 3 cm and a height of 4 cm. What is its slant height?
A) 5 cm
B) 7 cm
C) 12 cm
D) 25 cm
30. What is the sum of the interior angles of a pentagon?
A) 540°
B) 360°
C) 720°
D) 180°
31. A rectangular garden is 15 meters long and 8 meters wide. What is its area?
A) 120 sq. m
B) 23 sq. m
C) 30 sq. m
D) 46 sq. m
32. The perimeter of a square is 24 cm. What is its area?
A) 36 sq. cm
B) 12 sq. cm
C) 24 sq. cm
D) 6 sq. cm
33. What is the value of (sin(30°) + cos(60°)) / tan(45°)?
A) 1
B) 2
C) 0.5
D) 0
34. If tan(A) = 3/4 and tan(B) = 1/7, what is tan(A+B)?
A) 1
B) 2
C) 1/2
D) 3/4
35. What is the value of cot(90°)?
A) 0
B) 1
C) undefined
D) ∞
36. If a right-angled triangle has an angle θ such that sin(θ) = 3/5, what is cos(θ)?
A) 4/5
B) 5/4
C) 3/4
D) 5/3
37. What is the value of sec(0°)?
A) 1
B) 0
C) undefined
D) ∞
38. If tan(θ) = 1, what is the value of θ in degrees?
A) 45°
B) 30°
C) 60°
D) 90°
39. What is the value of sin²(θ) + cos²(θ)?
A) 1
B) 0
C) 2
D) sin(θ)cos(θ)
40. If cos(θ) = 1/2, what is the value of θ in degrees?
A) 60°
B) 30°
C) 45°
D) 90°
41. What is the value of tan(60°)?
A) √3
B) 1/√3
C) 2
D) 1/2
42. If sin(θ) = 3/5, what is cos(θ)?
A) 4/5
B) 5/4
C) 3/4
D) 5/3
43. The base and height of a parallelogram are 10 cm and 8 cm respectively. What is its area?
A) 80 sq. cm
B) 18 sq. cm
C) 40 sq. cm
D) 90 sq. cm
44. A sphere has a radius of 3 cm. What is its surface area?
A) 36π sq. cm
B) 12π sq. cm
C) 27π sq. cm
D) 9π sq. cm
45. What is the volume of a cube with a side length of 5 cm?
A) 125 cubic cm
B) 25 cubic cm
C) 150 cubic cm
D) 75 cubic cm
46. The perimeter of an equilateral triangle is 36 cm. What is its height?
A) 6√3 cm
B) 12 cm
C) 9√3 cm
D) 18 cm
47. A rectangle has an area of 96 sq. cm and a perimeter of 40 cm. What are its length and breadth?
A) 12 cm and 8 cm
B) 16 cm and 6 cm
C) 24 cm and 4 cm
D) 10 cm and 9.6 cm
48. The circumference of a circle is 44 cm. What is its radius?
A) 7 cm
B) 14 cm
C) 3.5 cm
D) 21 cm
49. A triangle has sides of length 3 cm, 4 cm, and 5 cm. What is its area?
A) 6 sq. cm
B) 12 sq. cm
C) 10 sq. cm
D) 8 sq. cm
50. The length and breadth of a rectangle are 12 cm and 5 cm respectively. What is the length of its diagonal?
A) 13 cm
B) 17 cm
C) 10 cm
D) 15 cm
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