Mathematics Partial Fractions Online Test

Maan AliLast Updated: October 15, 2025

Important Math Partial Fractions Question and Answer

Total Questions:	75
Time Allowed:	40 Minutes
Total Marks:	75
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Math Partial Fractions Practice Test Online With Explanation

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Page 1 of 3

Math

1. If x² + px + 1 is a factor of ax³ + bx + c, then

None of these

a² + c² = – ab

a² – c² = ab

a² – c² = – ab

2. The process of partial decomposition result in

Partial fraction

Equation

An identity

None of these

3. 1/(x²+x+a)(x²+x+b) =

None of these

1/a-b[1/x²+x+a – 1/x²+x+b]

1/a-b[1/x²+x+b +1/x²+x+a]

1/a-b[1/x²+x+b – 1/x²+x+a]

4. 9x²/x³¯¹ is a fraction.

Proper fraction

Improper fraction

Rational fraction

None of these

5. x-1/(x+2)(x-2) = ?

4/3(x-4) + 1/3(x-1)

3/x – 2/x+1

3/4(x+2) + 1/4(x-2)

4/3(x-2) + 4/3(x+2)

6. (x+2)² = x² + 4x + 4 is

A linear equation

None of these

A quadratic equation

A cubic equation

7. Partial fraction of x³+2x+2/(x²+x+1)² form

None of these

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

(Ax+B)(x²+x+1)+C(x²+x+1)²

A/x²+x+1 + B/(x²+x+1)²

8. ax+b/(cx + d)(ex +f) =

A/cx+d + Bx/(ex+f)²

None of these

Ax+B/cx+d + C/ex+f

A/cx+d + bx/ex+f

9. (ax+b)/(cx +d)² =

None of these

Ax+B/(cx+d)²

A/cx+d + B/(cx+d)²

A/cx+d + B/cx+d

10. 2x = 3 is a conditional equation it is true for

2/3

3/2

11. The symbol _________ shall be used both for equation and identity

≠

“=”

≡

12. (x – 4)² = x² – 8x + 16 is

Transcendental Equation

Cubic equation

Identity equation

An equation

13. (x + 2)² = x² + 4x + 4 is

Linear equation

An identity

Cubic equation

An equation

14. 1/(x – 3)(x – 2) =

1/x²-3 – 1/x²-2

1/x+3 – 1/x+2

1/x²-3 – 1/x-2

1/x-3 – 1/x-2

15. 10x-13/(x+2)(x-9) =

3/x-2 – 7/x+9

3/x+2 + 7/x-9

3/x-2 + 7/x+9

3/x+2 – 7/x-9

16. 4x = 5 is ?

Fraction

Conditional

Equation

Identity

17. In a quadratic equation with leading co-efficient 1, a student reads the co-efficient 16 of x wrongly as 19 and obtain the roots as – 15 and – 4. The correct roots are

6, 10

8, 8

-8, -8

-6, -10

18. Partial fractions of x/(x+a)(x+b)(x+c) will be of the form

A/x-a + B/x-b + C/x+c

None of these

A/x+a + B/x+b + C/x+c

A/x-a + B/x+b + C/x+c

19. Partial fractions of x²+1/x²+1 will be of the form

A/x+1 – B/x²-x+1

None of these

A/x-1 – B/x²-x+1

A/x+1 + Bx+C/x²-x+1

20. The partial fraction of 1/x²–1 is

1/(x–1)

1/2(x+1)

1/2(x–1) – 1/2(x+1)

1/2(x–1) + 1/2(x+1)

21. The rational fraction P(x)/Q(x) is a proper fraction if

Degree of P(x) = degree of Q(x)

Degree of Q(x)< degree of P(x)

None of these

Degree of P(x)< degree of Q(x)

22. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = -1, B = 1

A = x – 1, B = x + 1

A = 0, B = 2

A = x, B = 1

23. x-1/(x+2)(x-2) =

4/3(x-4) – 1/3(x-1)

2/3(x-2) – 4/3(x+2)

3/x – 2/x+1

3/4(x+2) + 1/4(x-2)

24. The identity (x + 3)(x + 4) = x² + 7x + 12 is true for

Two values of x

None of these

One value of x

All values of x

25. A fraction in which degree of numerator is less than degree of denominator is

A proper fraction

Algebric relation

Equation

An improper fraction

Page 2 of 3

26. If 2x¹ᐟ³ + 2 x¯¹ᐟ³ = 5, then x is equal to

1 or -1

4 or ¼

2 or ½

8 or 1/8

27. x + 3/x = 4 is

An equation

An identity

A transcendental equation

Cubic equation

28. An open sentence formed by using the sign of equality “=” is called

False Sentence

Equation

In Equation

True Sentence

29. Partial fractions of 2x⁴-3x³-4x/(x²+2)²(x+1)²

Ax+B/x²+2 + Cx+D/(x²+2)² + E/x+1 + F/(x+1)²

Ax+B/(x²+2)² + C/(x+1)²

None of these

A/(x²+2)² + B/(x+1)²

30. An improper fraction can be reduced to proper fraction by

Division

Addition

Subtraction

Multiplication

31. If x+p/(x-1)(x-3) = q/x-1 + 2/x-3, the value of P and Q are

P = 1, q = 1

P = 2, q = 1

P = 1, q = -1

P = -2, q = 1

32. x/(x+2)(x–3)

2/5(x+2) – 3/5(x+3)

2/5(x+2) + 3/5(x–3)

2/5(x–2) + 3/5(x+3)

2/5(x+2) – 3/5(x–3)

33. The value of k (k > 0) for which the equation x² – 8x + k = 0 both will have real roots is

– 16

– 64

34. A fraction in which the degree of the numerator is greater than or equal to the degree of the denominator is called

Algebraic equation

An improper fraction

Equation

A proper fraction

35. Which is a proper rational fraction?

2x²–5/x²+4

2x–5/x²+4

None of these

9x⁴/x³–1

36. 1/(x+3)(x+2) =

1/x+3 – 1/x+2

1/x-3 – 1/x-2

None of these

1/x²-3 – 1/x²-2

37. A relation in which the equality is true for any value of unknowns is called an

Algebric equation

Identity

Equation

Algebric relation

38. A fraction in which degree of numerator is greater than or equal to the degree of denominator is called

Improper fraction

Algebric equation

Equation

A proper fraction

39. Let the equation ax² – bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be

(4, 3, 2)

(6, 4, 1)

(5, 5, 1)

(5, 3, 1)

40. 1/(x²+5)(x²+5) =

1/x²-4 – 1/x²+5

1/x²+4 – 1/x²-5

None of these

1/x²+4 – 1/x²+5

41. Partial fractions of 2x²-3x+4/(x-1)³ will be of the form

A/x-1 + B/(x-1)² + C/(x-1)³

A/x-1 + Bx+C/(x-1)² + D/(x-1)³

Ax+B/x-1 + C/(x-1)² + D/(x-1)³

A/x+1 + B/(x+1)² + C/(x+1)³

42. x²–3/3x+1 is

Proper fraction

Rational fraction

None of these

Improper rational fraction

43. There are _________ types of rational fraction.

Four

Five

Two

Three

44. When two or more rational fractions are added, resulting fraction is called

None of these

Combined fraction

Partial fraction

Improper fraction

45. The function of the form f(x) = p(x)/q(x) q(x) ≠ 0 where P(x) and q(x) are polynomial in x is called

Identity

Fraction

Algebric relation

Equation

46. Partial fractions of 1/(x+1)(x²+1) will be the form

A/x-1 + B/x²+1

None of these

A/x+1 + Bx+C/x²+1

A/x+1 + B/x²+1

47. If a + b + c = 0, a ≠ 0, a, b, c ϵ Q, then both the roots of the equation ax² + bx + c = 0 are

Zero

Non-real

Irrational

Rational

48. A relation in which the quality is true only for a number of unknown is called

Identity

Algebric relation

Equation

Algebric equation

49. P(x)/Q(x), Q(x) ≠ 0 is known as

Proper rational fraction

None of these

Improper rational fraction

Rational fraction

50. Partial fractions of 1/(x + 1)(x² – 1)

A/x+1 + Bx+0/x²-1

A/x+1 + B/(x+1)² + C/x-1

A/x+1 + B/x+1 + C/x-1

None of these

Page 3 of 3

51. The set of real roots of the equation log(5x – 4) (2x+3)³ -log(2x + 3) (10x² + 23x + 12) = 1 is

Empty set

{-1}

{- 3/5}

{- 1/3}

52. x² + x – 6 = 0 is a conditional equation and it is true for

-2, -3

2, -3

2, 3

-2, 3

53. A relation in which equality is true for any value of unknown is called an

Algebric equation

Identity

Equation

None of these

54. 2x²-3x+4/(x+1)³ =

2/x+1 – 7/(x+1)² + 9/(x-1)³

2/x-1 – 7/(x+1)² + 9/(x+1)³

2/x-1 – 7/(x-1)² + 9/(x-1)³

2/x+1 – 7/(x+1)² + 9/(x+1)³

55. x + 3/x = 4 is

A transcendental equation

An equation

An identity

Cubic equation

56. Rotational fraction are of

Two types

Three types

One type

Four types

57. 2x-5/x²+4 is ___________ rational fraction

None of these

Improper

Proper

Conditional

58. Algebric equation can be divided into

One kind

Three kinds

Two kinds

Four kinds

59. Partial fractions of 1/x² -1 are equivalent to

A/x+1

A/x+1 + B/x-1

Ax+B/x²-1

B/x-1

60. If the roots of x² + ax + b = 0 are non-real, then for all real x, x² + ax + b is

Positive

Negative

Nothing can be said

Zero

61. The equation (cos P – 1) x² + x (cos P) + sin P = 0 in the variable x, has real roots, then P can take any value in the interval.

(0, π)

(-π/2, π/2)

(-π, 0)

(0, 2 π)

62. To resolve a combined fraction into its pars is called

None of these

Rational fraction

Combined fraction

Partial fraction

63. The number of solutions of the equation √y+3 + √y = 1 is

64. If 7x+25/(x+3)(x+4) = a/x+3 + B/x+4, then find values of A and B

A = 1, B = 5

A = 1, B = 3

A = 4, B = 3

A = 2, B = 3

65. The index of variables in a poly nomial is called its

Degree

Bare

Root

Co-efficient

66. Partial fractions of 1/(1–ax)(1–bx)(1–cx) will be of the form

A/1-ax + B/1-bx + C/1-cx

Ax+B/1-ax + C/1-bx + D/1-cx

None of these

A/1-ax + Bx+C/1-bx + D/1-cx

67. An open sentences formed by using the sign of equality “=” is called

Fraction

Equation

None of these

In equality

68. (x – 4)² = x² + 8x + 16 is

A transcendental equation

Cubic equation

An equation

An identity

69. Partial fractions of 1/x³+1 will be of the form

A/x-1 – B/x²-x+1

Ax+B/x+1 + C/x²-x+1

A/x+1 + Bx+C/x²-x+1

A/x+1 – B/x²-x+1

70. A quadratic factor which cannot be written as the product of two linear factors is called

Irreducible factor

None of these

Reducible factor

Re placed factor

71. If sin θ and cos θ are the roots of the equation ax² + bx + c = 0, then

(a + c)² = b² + c²

(a – c)² = b² – c²

(a – c)² = b² + c²

(a + c)² = b² – c²

72. The values of x which satisfy both the in equations x² – 1 ≤ 0 and x² – x 2 ≥ 0 lie is

(1, 2)

{-1}

(-1, 1)

(-1, 2)

73. A fraction in which the degree of the numerator is less than the degree of the denominator is called

Algebraic equation

An improper fraction

Equation

A proper fraction

74. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = -1, B = 1

A = x, B = 1

A = 0, B = 2

A = x-1, B = x + 1

75. Partial fractions of 1/x²-4 will be of the form

A/x+2 + B/x-2

A/x+2 + B/(x-2)²

A/x-2 + B/(x+2)²

None of these

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Maan AliLast Updated: October 15, 2025

Mathematics Partial Fractions Online Test

Important Math Partial Fractions Question and Answer

Math Partial Fractions Practice Test Online With Explanation

Math

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