1. Which of the following is a rational number between ¾ and ⅚?

• A) 7/12
• B) ⅘
• C) 9/10
• D) ⅝

2. The additive inverse of −5/7 is:

• A) 5/7
• B) −7/5
• C) 7/5
• D) −5/7

3. On the number line, where does −2/3 lie relative to 0 and −1?

• A) To the left of −1
• B) Between 0 and −1
• C) To the right of 0
• D) At −1

4. Solve for x: 2x + 5 = 11.

• A) x = 2
• B) x = 3
• C) x = 4
• D) x = 5

5. If the cost of 3 pens is ₹15, how much will 5 pens cost?

• A) ₹20
• B) ₹25
• C) ₹30
• D) ₹35

6. The solution to 3(x − 2) = 9 is:

• A) x = 3
• B) x = 4
• C) x = 5
• D) x = 6

7. The opposite angles of a parallelogram are:

• A) Equal
• B) Complementary
• C) Supplementary
• D) Unequal

8. In a square, the measure of each interior angle is:

• A) 90°
• B) 120°
• C) 135°
• D) 180°

9. A quadrilateral with only one pair of parallel sides is called a:

• A) Rectangle
• B) Rhombus
• C) Trapezium
• D) Parallelogram

10. To construct a quadrilateral, the minimum number of measurements required is:

• A) 3
• B) 4
• C) 5
• D) 6

11. In constructing a triangle, which set of measurements is sufficient?

• A) Two sides and one angle
• B) Two angles and one side
• C) Three angles
• D) One side and one angle

12. A quadrilateral can be constructed uniquely if we know its:

• A) Four sides
• B) Four angles
• C) Three sides and two included angles
• D) Two sides and three angles

13. In a histogram, the height of each bar represents:

• A) Class interval
• B) Frequency
• C) Midpoint
• D) Width

14. The probability of getting a head when tossing a fair coin is:

• A) ¼
• B) ⅓
• C) ½
• D) 1

15. A bar graph is used to represent:

• A) Continuous data
• B) Categorical data
• C) Time-series data
• D) Frequency distribution

16. The square root of 144 using prime factorization is:

• A) 10
• B) 12
• C) 14
• D) 16

17. Which number is a perfect square?

• A) 50
• B) 64
• C) 72
• D) 80

18. The square of 15 is:

• A) 200
• B) 225
• C) 250
• D) 275

19. The cube root of 27 is:

• A) 2
• B) 3
• C) 4
• D) 5

20. Which number is a perfect cube?

• A) 100
• B) 125
• C) 150
• D) 200

21. The cube of 4 is:

• A) 16
• B) 32
• C) 64
• D) 128

22. A shopkeeper sells an item for ₹1200 with a 20% profit. The cost price is:

• A) ₹960
• B) ₹1000
• C) ₹1080
• D) ₹1100

23. The simple interest on ₹5000 at 5% per annum for 2 years is:

• A) ₹500
• B) ₹600
• C) ₹700
• D) ₹800

24. A discount of 10% on an item of ₹1000 results in a selling price of:

• A) ₹900
• B) ₹950
• C) ₹1000
• D) ₹1100

25. Simplify (2x + 3)(x + 2) using the identity.

• A) 2x² + 7x + 6
• B) 2x² + 6x + 5
• C) 2x² + 5x + 6
• D) 2x² + 7x + 5

26. Using the identity (a + b)², simplify (3x + 4)².

• A) 9x² + 16
• B) 9x² + 24x + 16
• C) 9x² + 12x + 16
• D) 9x² + 24x + 12

27. The product of (x − 2) and (x + 2) is:

• A) x² − 4
• B) x² + 4
• C) x² − 2x + 4
• D) x² + 2x − 4

28. The number of faces in a cuboid is:

• A) 4
• B) 6
• C) 8
• D) 12

29. Euler’s formula for a polyhedron is:

• A) F + V = E + 2
• B) F + E = V + 2
• C) V + E = F + 2
• D) F + V = E

30. A cylinder has how many curved surfaces?

• A) 1
• B) 2
• C) 3
• D) 4

31. The area of a trapezium with parallel sides 6 cm and 4 cm and height 5 cm is:

• A) 25 cm²
• B) 30 cm²
• C) 35 cm²
• D) 40 cm²

32. The volume of a cuboid with dimensions 5 cm, 4 cm, and 3 cm is:

• A) 60 cm³
• B) 70 cm³
• C) 80 cm³
• D) 90 cm³

33. The surface area of a cube with side 4 cm is:

• A) 64 cm²
• B) 96 cm²
• C) 128 cm²
• D) 160 cm²

34. Simplify 2³ × 2².

• A) 2⁴
• B) 2⁵
• C) 2⁶
• D) 2⁷

35. Express 0.00032 in standard form.

• A) 3.2 × 10⁻⁴
• B) 3.2 × 10⁻⁵
• C) 3.2 × 10⁴
• D) 3.2 × 10⁵

36. The value of (3⁻²)⁻¹ is:

• A) 1/9
• B) 1/3
• C) 3
• D) 9

37. If 4 workers complete a task in 12 days, how many days will 6 workers take?

• A) 8 days
• B) 10 days
• C) 12 days
• D) 14 days

38. If x and y are in direct proportion and x = 10 when y = 20, what is y when x = 15?

• A) 25
• B) 30
• C) 35
• D) 40

39. If the speed of a car increases, the time taken to cover a fixed distance:

• A) Increases
• B) Decreases
• C) Remains the same
• D) Doubles

40. Factorize x² + 5x + 6.

• A) (x + 2)(x + 3)
• B) (x + 1)(x + 6)
• C) (x + 3)(x + 2)
• D) (x + 1)(x + 5)

41. Using the identity a² − b², factorize 9x² − 16.

• A) (3x − 4)(3x + 4)
• B) (3x − 4)²
• C) (3x + 4)²
• D) (9x − 16)(9x + 16)

42. The factors of 2x² + 7x + 3 are:

• A) (2x + 1)(x + 3)
• B) (x + 1)(2x + 3)
• C) (2x + 3)(x + 1)
• D) (x + 3)(2x + 1)

43. The slope of the line y = 2x + 3 is:

• A) 1
• B) 2
• C) 3
• D) 4

44. The point where a linear graph intersects the x-axis has a y-coordinate of:

• A) 0
• B) 1
• C) −1
• D) Undefined

45. If a graph represents direct proportion, it is a:

• A) Straight line through origin
• B) Parabola
• C) Circle
• D) Hyperbola

46. Which of the following is an irrational number?

• A) 0.6
• B) √3
• C) 7/8
• D) 1.2

47. Simplify (2³ × 2²) ÷ 2⁴.

• A) 2
• B) 4
• C) 8
• D) 16

48. The decimal expansion of 1/5 is:

• A) Terminating
• B) Non-terminating repeating
• C) Non-terminating non-repeating
• D) Irrational

49. On the number line, √2 lies between:

• A) 1 and 2
• B) 2 and 3
• C) 3 and 4
• D) 4 and 5

50. The degree of the polynomial 3x⁴ − 2x² + 5 is:

• A) 2
• B) 3
• C) 4
• D) 5