GENERAL MATHEMATICS (CORE) 2024/2025 Trial Test Questions (30) Objective Questions

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Select the correct options for each Questions below

1. Solve for x: 3x - 2 = 4x + 1

a) x = -3 b) x = -1 c) x = 2 d) x = 3

2. Factorize the expression: 4x^2 - 16

a) (2x - 4)(2x + 4) b) (2x - 2)(2x + 2) c) (x - 4)(x + 4) d) (x - 2)(x + 2)

3. Simplify: (2x^3y^2) / (4x^2y^3)

a) 1/2x b) 1/2y c) x/y d) y/x

4. If 2x + 3y = 12 and 3x - y = 6, find the values of x and y.

a) x = 3, y = 2 b) x = 4, y = 3 c) x = 2, y = 3 d) x = 1, y = 5

5. Solve the equation: 2(x + 1) - 3(2x - 5) = 4

a) x = -3 b) x = 2 c) x = 1 d) x = -1

6. Find the area of a triangle with base 6 cm and height 8 cm.

a) 24 cm² b) 30 cm² c) 20 cm² d) 18 cm²

7. Given a rectangle with length 10 cm and width 4 cm, find the perimeter.

a) 28 cm b) 40 cm c) 18 cm d) 14 cm

8. Calculate the circumference of a circle with a radius of 5 cm.

a) 15.7 cm b) 31.4 cm c) 10 cm d) 20 cm

9. Calculate the volume of a cylinder with a radius of 4 cm and height of 10 cm.

a) 160π cm³ b) 40π cm³ c) 320 cm³ d) 80π cm³

10. Solve for x: 2x^2 - 5x + 3 = 0

a) x = 3, x = 1/2 b) x = 2, x = 1/3 c) x = 1, x = 3 d) x = 3, x = 1

11. If a + b = 10 and a - b = 4, find the values of a and b.

a) a = 7, b = 3 b) a = 6, b = 4 c) a = 8, b = 2 d) a = 5, b = 5

12. Calculate the value of x in the equation 2(x + 3) = 7x - 6.

a) x = 2 b) x = 3 c) x = 4 d) x = 5

13. Find the value of y in the equation 3y - 5 = 4y + 7.

a) y = -12 b) y = 12 c) y = -6 d) y = 6

14. If 2x - 3 = 7, find the value of x.

a) x = 10 b) x = 5 c) x = 6 d) x = 7

15. Simplify: (3x^2y^3) / (6x^2y^2).

a) 1/2y b) 1/2x c) x/y d) y/x

16. Calculate the area of a trapezoid with a base of 8 cm, another base of 12 cm, and a height of 6 cm.

a) 60 cm² b) 100 cm² c) 80 cm² d) 48 cm²

17. Determine the volume of a sphere with a radius of 5 cm.

a) 523.6 cm³ b) 1047.2 cm³ c) 157.08 cm³ d) 209.44 cm³

18. Solve for the missing side in a right triangle: Given one leg as 5 cm and the hypotenuse as 13 cm.

a) 12 cm b) 8 cm c) 15 cm d) 10 cm

19. Find the area of a circle with a radius of 6 cm.

a) 36π cm² b) 72π cm² c) 12π cm² d) 18π cm²

20. Calculate the surface area of a rectangular prism with dimensions: length = 8 cm, width = 4 cm, and height = 6 cm.

a) 200 cm² b) 144 cm² c) 184 cm² d) 208 cm²

21. Find the sine, cosine, and tangent of an angle θ where sin(θ) = 0.6 and θ is in the first quadrant.

a) sin(θ) = 0.6, cos(θ) = 0.8, tan(θ) = 0.75 b) sin(θ) = 0.6, cos(θ) = 0.4, tan(θ) = 1.5 c) sin(θ) = 0.6, cos(θ) = 0.3, tan(θ) = 2 d) sin(θ) = 0.6, cos(θ) = 0.6, tan(θ) = 1

22. Calculate the value of θ in a right triangle where opposite side = 5 and adjacent side = 12.

a) θ ≈ 22.6° b) θ ≈ 67.4° c) θ ≈ 45° d) θ ≈ 33.7°

23. Find the exact value of sin(45°) in terms of a fraction.

a) 1/2 b) √2/2 c) √3/2 d) 3/2

24. Calculate the value of cos(60°) in terms of a fraction.

a) 1/2 b) √2/2 c) √3/2 d) 3/2

25. Determine the value of tan(30°) in terms of a fraction.

a) 1/2 b) √2/2 c) √3/3 d) 3/2

26. In a triangle, if one angle is 30° and another is 60°, what is the measure of the third angle?

a) 30° b) 45° c) 60° d) 90°

27. If sin(θ) = 0.8 and θ is in the first quadrant, what is the value of cos(θ)?

a) cos(θ) = 0.6 b) cos(θ) = 0.4 c) cos(θ) = 0.2 d) cos(θ) = 0.9

28. If tan(θ) = 2 and θ is in the second quadrant, what is the value of sin(θ)?

a) sin(θ) = 1/√5 b) sin(θ) = -1/√5 c) sin(θ) = 2/√5 d) sin(θ) = -2/√5

29. Solve for θ: sin(θ) = 0.7071 (rounded to four decimal places).

a) θ ≈ 45° b) θ ≈ 60° c) θ ≈ 30° d) θ ≈ 75°

30. Calculate the value of cos(120°) in terms of a fraction.

a) -1/2 b) -√3/2 c) -1 d) -√2/2