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1. The factorisation of 12a²b + 15ab² gives:
A. 3ab(4ab + 5)
B. 3ab(4a + 5b)
C. 3a(4a + 5b)
D. 3b(4a + 5b)
Answer: B

2. The factorisation of 12x + 36 is:
A. 12(x + 3)
B. 12(3x)
C. 12(3x + 1)
D. x(12 + 36x)
Answer: A

3. On factorising 14pq + 35pqr, we get:
A. pq(14 + 35r)
B. p(14q + 35qr)
C. q(14p + 35pr)
D. 7pq(2 + 5r)
Answer: D

4. The factors of 6xy – 4y + 6 – 9x are:
A. (3x + 2)(2y + 3)
B. (3x – 2)(2y – 3)
C. (3x – 2)(2y + 3)
D. (3x + 2)(2y – 3)
Answer: B

5. The factors of x² + xy + 8x + 8y are:
A. (x + y)(x + 8)
B. (2x + y)(x + 8)
C. (x + 2y)(x + 8)
D. (x + y)(2x + 8)
Answer: A

6. The factors of 4y² – 12y + 9 is:
A. (2y + 3)²
B. (2y – 3)²
C. (2y – 3)(2y + 3)
D. None of the above
Answer: B

7. The factors of 49p² – 36 are:
A. (7p + 6)²
B. (7p – 6)²
C. (7p – 6)(7p + 6)
D. None of the above
Answer: C

8. The factors of m² – 256 are:
A. (m + 4)²
B. (m – 4)²
C. (m – 4)(m + 4)
D. None of the above
Answer: D

9. When we factorise x² + 5x + 6, then we get:
A. (x + 2)(x + 3)
B. (x – 2)(x – 3)
C. (x × 2) + (x × 3)
D. (x × 2) – (x × 3)
Answer: A

10. The factors of 3m² + 9m + 6 are:
A. (m + 1)(m + 2)
B. 3(m + 1)(m + 2)
C. 6(m + 1)(m + 2)
D. 9(m + 1)(m + 2)
Answer: B

11. The common factor of a³b³ and ab² is:
A. a²b²
B. ab²
C. a²b
D. ab
Answer: B

12. The common factor of a³b² and a⁴b is:
A. a⁴b²
B. a⁴b
C. a³b²
D. a³b
Answer: D

13. The common factor 12a and 30 is:
A. 6
B. 12
C. 30
D. 6a
Answer: A

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14. The common factors of 10a, 20b and 30c are:
A. ab
B. ac
C. 10abc
D. 10
Answer: D

15. The common factor of 6x³y⁴z², 21x²y and 15x³ is:
A. 3x²
B. 3x³
C. 6x³
D. 6x²
Answer: A

16. The common factor of 24a³b⁴, 36a⁴c⁴ and 48a³b²c is:
A. 12a³
B. 24a³
C. 36a³
D. 48a³
Answer:

17. The factorisation of 12x²y + 15xy² is:
A. 3xy²(4x + 5y)
B. 3x²y(4x + 5y)
C. 3xy(4x + 5y)
D. 3x²y²(4x + 5y)
Answer: C

18. The factorisation of 5x – 20 is:
A. 5(x – 5)
B. 5(x – 4)
C. 5(x – 3)
D. 5(x – 20)
Answer: B

19. The factorisation of 8x + 4y is:
A. 8(x + 4y)
B. 4(2x + 4y)
C. 8(x + y)
D. 4(2x + y)
Answer: D

20. The factors of xyz are:
A. x
B. y
C. z
D. All of the above
Answer: D

21. The common factor of x²y² and x³y³ is:
A. x²y²
B. x³y³
C. x²y³
D. x³y²
Answer: A

22. The common factor of x³y² and x⁴y is:
A. x⁴y
B. x³y²
C. x³y
D. None of the above
Answer: C

23. The common factor of a²m⁴ and a⁴m² is:
A. a⁴m⁴
B. a²m²
C. a²m⁴
D. a⁴m²
Answer: B

24. The common factor of p³q⁴ and p⁴q³ is:
A. p⁴q
B. p³q²
C. p³q³
D. p²q⁴
Answer: C

25. The common factor 12y and 30 is:
A. 6
B. 12
C. 30
D. 6y
Answer: A

26. The common factor of 2x, 3x³, 4 is:
A. 1
B. 2
C. 3
D. 4
Answer: A

27. The common factor of 10ab, 30bc, 50ca is:
A. 10
B. 30
C. 50
D. abc
Answer: A

28. The common factor of 14a²b and 35a⁴b² is:
A. a⁴b²
B. 35a⁴b²
C. 14a²b
D. 7a²b
Answer: D

29. The common factor of 8a²b⁴c², 12a⁴bc⁴ and 20a³b⁴ is:
A. a⁴b⁴
B. a²b²
C. 4a²b
D. 4a²b²
Answer: D

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30. The common factor of 6a³b⁴c², 21a²b and 15a³ is:
A. 3a²
B. 3a³
C. 6a³
D. 6a²
Answer: A

31. The common factor of 2a²b⁴c², 8a⁴b³c⁴ and 6a³b⁴c² is:
A. 2a²b³c²
B. 6a²b³c²
C. 8a²b³c²
D. None of the above
Answer: A

32. The common factor of 3a²b⁴c², 12b²c⁴ and 15a³b⁴c⁴ is:
A. b⁴c⁴
B. 3b²c²
C. 15b²c⁴
D. 12b²c⁴
Answer: B

33. The common factor of 24x³y⁴, 36x⁴z⁴ and 48x³y²z is:
A. 12x³
B. 24x³
C. 36x³
D. 48x³
Answer: A

34. The common factor of 72x³y⁴z⁴, 120z²d⁴x⁴ and 96y³z⁴d⁴ is:
A. 96z³
B. 120z³
C. 72z³
D. 24z²
Answer: D

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35. The common factor of 36p²q³x⁴, 48pq³x² and 54p³q³x⁴ is:
A. 6pq³x²
B. 36pq³x²
C. 54pq³x²
D. 48pq³x²
Answer: A

36. The factorisation of 12a²b + 15ab² is:
A. 3ab(4a + 5b)
B. 3a²b(4a + 5b)
C. 3ab²(4a + 5b)
D. None of the above
Answer: A

37. The factorisation of 10x² – 18x³ + 14x⁴ is:
A. 2x²(7x² – 9x + 5)
B. 2x(7x² – 9x + 5)
C. 2(7x² – 9x + 5)
D. 2x³(7x² – 9x + 5)
Answer: A

38. The factorisation of 6x – 42 is:
A. 6(x – 7)
B. 3(x – 7)
C. 2(x – 7)
D. 6(x + 7)
Answer: A

39. The factorisation of 6x + 12y is:
A. 6(x + 2y)
B. 3(x + 4y)
C. 2(3x + 12y)
D. None of these
Answer: A

40. The factorisation of 28a³b⁵ – 42a⁵b³ is:
A. 14a³b³(2b² – 3a²)
B. 14a²b³(2b² – 3a²)
C. 14a³b²(2b² – 3a²)
D. None of these
Answer: A

41. The factorisation of a³ + a²b + ab² is:
A. a(a² + ab + b²)
B. 6(a² + ab + b²)
C. ab(a² + ab + b²)
D. None of these
Answer: A

42. The factorisation of x²yz + xy²z + xyz² is:
A. xyz(x + y + z)
B. x²yz(x + y + z)
C. xy²z(x + y + z)
D. xyz²(x + y + z)
Answer: A

43. The factorisation of ax²y + bxy² + cxyz is:
A. xy(ax + by + cz)
B. axy(ax + by + cz)
C. bxy(ax + by + cz)
D. cxy(ax + by + cz)
Answer: A

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44. The factorisation of a(x + y + z) + b(x + y + z) + c(x + y + z) is:
A. (a + b + c)(x + y + z)
B. (ab + bc + ca)(x + y + z)
C. (xy + yz + zx)(a + b + c)
D. None of these
Answer: A

45. The factorisation of 6xy – 4y + 6 – 9x is:
A. (3x – 2)(2y – 3)
B. (3x + 2)(2y – 3)
C. (3x – 2)(2y + 3)
D. (3x + 2)(2y + 3)
Answer: A

46. The factorisation of x² + xy + 2x + 2y is:
A. (x + 2)(x + y)
B. (x + 2)(x – y)
C. (x – 2)(x + y)
D. (x – 2)(x – y)
Answer: A

47. The factorisation of ax + bx – ay – by is:
A. (x – y)(a + b)
B. (x + y)(a + b)
C. (x – y)(a – b)
D. (x + y)(a – b)
Answer: A

48. The factorisation of ab – a – b + 1 is:
A. (a – 1)(b – 1)
B. (a + 1)(b + 1)
C. (a – 1)(b + 1)
D. (a + 1)(b – 1)
Answer: A

49. The factorisation of x² + x + xy + y + zx + z is:
A. (x + y + z)(x + 1)
B. (x + y + z)(x + y)
C. (x + y + z)(y + z)
D. (x + y + z)(z + x)
Answer: A

50. The factorisation of x² + 8x + 16 is:
A. (x + 2)²
B. (x + 4)²
C. (x – 2)²
D. (x – A)²
Answer: B

51. The factorisation of 4y² – 12y + 9 is:
A. (2y + 3)²
B. (2y – 3)²
C. (3y + 2)²
D. (3y – 2)²
Answer: B

52. The factorisation of 49p² – 36 is:
A. (7p + 6)(7p – 6)
B. (6p + 7)(6p – 7)
C. (7p + 6)²
D. (7p – 6)²
Answer: A

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53. The factorisation of y² – 7y + 12 is:
A. (y + 3)(y + 4)
B. (y + 3)(y – 4)
C. (y – 3)(y + 4)
D. (y – 3)(y – 4)
Answer: D

54. The factorisation of z² – 4z – 12 is:
A. (z + 6)(z + 2)
B. (z – 6)(z – 2)
C. (z – 6)(z + 2)
D. (z + 6)(z – 2)
Answer: C

55. The factorisation of am² + bm² + bn² + an² is:
A. (a + b)(m² – n²)
B. (a + b)(m² + n²)
C. (a – b)(m² + n²)
D. (a – b)(m² – n²)
Answer: B

56. The factorisation of (lm + l) + m + 1 is:
A. (l + 1)(m + 1)
B. (l – 1)(m – 1)
C. (l + 1)(m – 1)
D. (l – 1)(m + 1)
Answer: A

57. The factorisation of (l + m)² – 4lm is:
A. (l – m)²
B. (l + m – 2)²
C. (l + m + 2)²
D. None of these
Answer: A

58. The factorisation of 1 + p + q + r + pq + qr + pr + pqr is:
A. (1 + p)(1 + q)(1 + r)
B. (1 – p)(1 – q)(1 – r)
C. (1 – p)(1 – q)(1 + r)
D. (1 + p)(1 – q)(1 – r)
Answer: A

59. The value of 0.645 × 0.645 + 2 × 0.645 × 0.355 + 0.355 × 0.355 is:
A. 1
B. 0
C. -1
D. 2
Answer: A

60. The factorisation of 1 + 16x + 64x² is:
A. (1 – 8x)²
B. (1 + 8x)²
C. (8 – x)²
D. (8 + x)²
Answer: B

61. The factorisation of x² + x + 14 is:
A. (x² – 1)²
B. (x² + 1)²
C. (x + 12)²
D. (x – 12)²
Answer: C

62. The value of 992 is:
A. (90)² + 2(90)(9) + (9)²
B. (90)² – 2(90)(9) + (9)²
C. (90)² + (9)²
D. None of these
Answer: A

63. The value of 492 is:
A. (50)² – 2(50)(1) + (1)²
B. (50)² + 2(50)(1) + (1)²
C. (50)² – (1)²
D. (50)² + (1)²
Answer: A

64. The factorisation of (x²y² – 2 + y²x²), x ≠ 0, y ≠ 0 is:
A. (xy + yx)²
B. (xy – yx)²
C. (xy – 1)²
D. (xy + 1)²
Answer: B

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65. The value of 0.73 × 0.73 × −0.27 × 0.270.73 − 0.27 is:
A. 1
B. 0
C. 0.73
D. 0.27
Answer: A

66. The factorisation of x² – 9 is:
A. (x – 3)²
B. (x + 3)²
C. (x + 3)(x – 3)
D. None of these
Answer: C

67. The factorisation of 36x²y² – 1 is:
A. (6xy – 1)(6xy + 1)
B. (6xy – 1)²
C. (6xy + 1)²
D. (6 + xy)²
Answer: A

68. The value of 0.564 × 0.564 × −0.436 × 0.4360.564 − 0.436 is:
A. 0
B. 1
C. -1
D. None of these
Answer: B

69. The value of (0.68)² – (0.32)² is:
A. -1
B. 0
C. 1
D. 0.36
Answer: D

70. The factorisation of 3x² + 10x + 8 is:
A. (3x + 4)(x + 2)
B. (3x – 4)(x – 2)
C. (3x + 4)(x – 2)
D. (3x – 4)(x + 2)
Answer: A

71. The factorisation of 3x² – 16x + 16 is:
A. (x – 4)(3x – 4)
B. (x + 4)(3x + 4)
C. (x – 4)(3x + 4)
D. (x + 4)(3x – 4)
Answer: A

72. The factorisation of 6x² – 5x – 6 is:
A. (2x – 3)(3x + 2)
B. (2x + 3)(3x + 2)
C. (2x – 3)(3x – 2)
D. (2x + 3)(3x – 2)
Answer: A

73. The factorisation of 6 – x – 2x² is:
A. (2 + x)(3 – 2x)
B. (2 + x)(3 + 2x)
C. (2 – x)(3 – 2x)
D. (2 – x)(3 + 2x)
Answer: A

74. If x² – x – 42 = (x + k)(x + 6), then k =:
A. 6
B. -6
C. 7
D. -7
Answer: D

75. The value of 3.5 × 3.5 – 2.5 × 2.5 is:
A. -6
B. 6
C. 60
D. 1
Answer: B

78. The quotient of 28x² + 14x is:
A. 2
B. 2x
C. x
D. x²
Answer: B

79. The quotient of 12a⁸b⁸ + (-a⁶b⁶) is:
A. 3a²b²
B. 3a²b
C. 3ab²
D. -3a²b²
Answer: D

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