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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
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Math Partial Fractions Practice Test Online With Explanation

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Page 1 of 3

Math

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

A = x, B = 1

A = 0, B = 2

A = -1, B = 1

A = x – 1, B = x + 1

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

4/3(x-4) – 1/3(x-1)

2/3(x-2) – 4/3(x+2)

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

3/x – 2/x+1

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

– 16

– 64

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

None of these

Conditional

Improper

Proper

5. 2x = 3 is a conditional equation it is true for

3/2

2/3

6. 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)

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

Rational

Zero

Irrational

Non-real

8. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = 0, B = 2

A = x, B = 1

A = -1, B = 1

A = x-1, B = x + 1

9. 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

(5, 3, 1)

(5, 5, 1)

(6, 4, 1)

(4, 3, 2)

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

None of these

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

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

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

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

A/x+1 + Bx+0/x²-1

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

None of these

A/x+1 + B/(x+1)² + C/x-1

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

Algebric equation

Algebric relation

Equation

Identity

13. 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

14. Rotational fraction are of

Three types

Two types

Four types

One type

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

None of these

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

A/(x²+2)² + B/(x+1)²

Ax+B/(x²+2)² + C/(x+1)²

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

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

A/x-1 + B/(x-1)² + C/(x-1)³

17. 1/(x+3)(x+2) =

None of these

1/x-3 – 1/x-2

1/x²-3 – 1/x²-2

1/x+3 – 1/x+2

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

A/x+1

Ax+B/x²-1

B/x-1

A/x+1 + B/x-1

19. 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

20. x + 3/x = 4 is

Cubic equation

An identity

A transcendental equation

An equation

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

4 or ¼

1 or -1

8 or 1/8

2 or ½

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

In equality

Equation

Fraction

None of these

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

-2, -3

2, -3

-2, 3

2, 3

24. 9x²/x³¯¹ is a fraction.

Improper fraction

Proper fraction

None of these

Rational fraction

25. There are _________ types of rational fraction.

Four

Two

Three

Five

Page 2 of 3

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

Algebraic equation

A proper fraction

An improper fraction

Equation

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

In Equation

Equation

False Sentence

True Sentence

28. 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, 0)

(-π/2, π/2)

(0, 2 π)

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

Equation

Algebraic equation

A proper fraction

An improper fraction

30. 1/(x²+x+a)(x²+x+b) =

None of these

1/a-b[1/x²+x+b – 1/x²+x+a]

1/a-b[1/x²+x+a – 1/x²+x+b]

1/a-b[1/x²+x+b +1/x²+x+a]

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

None of these

A/x+2 + B/x-2

A/x-2 + B/(x+2)²

A/x+2 + B/(x-2)²

32. (x + 2)² = x² + 4x + 4 is

An equation

An identity

Cubic equation

Linear equation

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

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

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

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

None of these

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

Division

Addition

Subtraction

Multiplication

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

(Ax+B)(x²+x+1)+C(x²+x+1)²

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

None of these

A/x²+x+1 + B/(x²+x+1)²

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

None of these

Identity

Algebric equation

Equation

37. Algebric equation can be divided into

Three kinds

One kind

Four kinds

Two kinds

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

39. P(x)/Q(x), Q(x) ≠ 0 is known as

None of these

Improper rational fraction

Rational fraction

Proper rational fraction

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

A = 2, B = 3

A = 1, B = 3

A = 4, B = 3

A = 1, B = 5

41. 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

42. 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

43. (x – 4)² = x² – 8x + 16 is

An equation

Transcendental Equation

Cubic equation

Identity equation

44. The process of partial decomposition result in

An identity

Equation

None of these

Partial fraction

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

a² – c² = ab

None of these

a² – c² = – ab

a² + c² = – ab

46. 1/(x – 3)(x – 2) =

1/x+3 – 1/x+2

1/x²-3 – 1/x-2

1/x²-3 – 1/x²-2

1/x-3 – 1/x-2

47. (x+2)² = x² + 4x + 4 is

A quadratic equation

A linear equation

A cubic equation

None of these

48. 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

49. (x – 4)² = x² + 8x + 16 is

A transcendental equation

An equation

Cubic equation

An identity

50. x²–3/3x+1 is

Improper rational fraction

Rational fraction

Proper fraction

None of these

Page 3 of 3

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

≠

“=”

≡

52. (ax+b)/(cx +d)² =

A/cx+d + B/cx+d

None of these

A/cx+d + B/(cx+d)²

Ax+B/(cx+d)²

53. x + 3/x = 4 is

An identity

A transcendental equation

Cubic equation

An equation

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

Root

Bare

Co-efficient

Degree

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

Reducible factor

None of these

Irreducible factor

Re placed factor

56. 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)

57. 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

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

A proper fraction

Equation

Improper fraction

Algebric equation

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

A/cx+d + bx/ex+f

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

None of these

A/cx+d + Bx/(ex+f)²

60. Which is a proper rational fraction?

9x⁴/x³–1

2x–5/x²+4

None of these

2x²–5/x²+4

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

{- 3/5}

Empty set

{-1}

{- 1/3}

62. 4x = 5 is ?

Equation

Conditional

Fraction

Identity

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

A/x-1 – B/x²-x+1

A/x+1 – B/x²-x+1

A/x+1 + Bx+C/x²-x+1

Ax+B/x+1 + C/x²-x+1

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

Algebric equation

Algebric relation

Equation

Identity

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

None of these

A/x-1 + B/x²+1

A/x+1 + B/x²+1

A/x+1 + Bx+C/x²+1

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

Rational fraction

Combined fraction

None of these

Partial fraction

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

Improper fraction

None of these

Combined fraction

Partial fraction

68. 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

Algebric relation

Equation

Identity

Fraction

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

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

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

3/x – 2/x+1

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

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

An improper fraction

Equation

Algebric relation

A proper fraction

71. 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 = -2, q = 1

P = 1, q = -1

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

Two values of x

One value of x

All values of x

None of these

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

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

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

None of these

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

74. The partial fraction of 1/x²–1 is

1/2(x–1) + 1/2(x+1)

1/(x–1)

1/2(x–1) – 1/2(x+1)

1/2(x+1)

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

Zero

Negative

Positive

Nothing can be said

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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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