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 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

2. There are _________ types of rational fraction.

Three

Four

Two

Five

3. 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

4. 9x²/x³¯¹ is a fraction.

Proper fraction

Improper fraction

None of these

Rational fraction

5. Which is a proper rational fraction?

2x–5/x²+4

2x²–5/x²+4

None of these

9x⁴/x³–1

6. 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)

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

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

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

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

3/x – 2/x+1

8. 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

Fraction

Identity

Equation

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

Equation

Identity

Algebric equation

Algebric relation

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

Rational fraction

Combined fraction

Partial fraction

None of these

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

An improper fraction

Algebraic equation

Equation

A proper fraction

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

≡

≠

“=”

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

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

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

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

None of these

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

A proper fraction

Improper fraction

Equation

Algebric equation

15. (x+2)² = x² + 4x + 4 is

A cubic equation

A quadratic equation

A linear equation

None of these

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

(-1, 1)

(-1, 2)

{-1}

(1, 2)

17. x + 3/x = 4 is

A transcendental equation

An equation

Cubic equation

An identity

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

Combined fraction

Partial fraction

Improper fraction

None of these

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

P = -2, q = 1

P = 1, q = 1

P = 1, q = -1

P = 2, q = 1

20. 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, 2 π)

(-π, 0)

(0, π)

(-π/2, π/2)

21. 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

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

Equation

None of these

Fraction

In equality

23. 1/(x²+x+a)(x²+x+b) =

1/a-b[1/x²+x+a – 1/x²+x+b]

1/a-b[1/x²+x+b – 1/x²+x+a]

None of these

1/a-b[1/x²+x+b +1/x²+x+a]

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

A/x²+x+1 + B/(x²+x+1)²

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

(Ax+B)(x²+x+1)+C(x²+x+1)²

None of these

25. (x – 4)² = x² – 8x + 16 is

Transcendental Equation

Identity equation

An equation

Cubic equation

Page 2 of 3

26. x²–3/3x+1 is

Improper rational fraction

None of these

Proper fraction

Rational fraction

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

Identity

Algebric relation

Algebric equation

Equation

28. 2x-5/x²+4 is ___________ rational fraction

Improper

Conditional

None of these

Proper

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

30. 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)

(5, 5, 1)

(5, 3, 1)

(6, 4, 1)

31. (x + 2)² = x² + 4x + 4 is

An identity

Cubic equation

Linear equation

An equation

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

A/x+1 + B/x²+1

None of these

A/x-1 + B/x²+1

A/x+1 + Bx+C/x²+1

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

{-1}

{- 3/5}

{- 1/3}

Empty set

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

None of these

A/(x²+2)² + B/(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

35. (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

36. x + 3/x = 4 is

An identity

A transcendental equation

An equation

Cubic equation

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

None of these

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

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

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

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

All values of x

None of these

One value of x

Two values of x

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

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

None of these

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

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

40. 4x = 5 is ?

Identity

Equation

Fraction

Conditional

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

An improper fraction

Algebric relation

A proper fraction

Equation

42. 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

Rational

Irrational

43. P(x)/Q(x), Q(x) ≠ 0 is known as

Improper rational fraction

None of these

Proper rational fraction

Rational fraction

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

Nothing can be said

Negative

Zero

Positive

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

4 or ¼

2 or ½

1 or -1

8 or 1/8

46. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = 0, B = 2

A = x-1, B = x + 1

A = -1, B = 1

A = x, B = 1

47. 2x = 3 is a conditional equation it is true for

2/3

3/2

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

Reducible factor

Re placed factor

None of these

Irreducible factor

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

a² + c² = – ab

a² – c² = ab

a² – c² = – ab

None of these

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

Degree

Root

Co-efficient

Bare

Page 3 of 3

51. Algebric equation can be divided into

Four kinds

Two kinds

One kind

Three kinds

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

-2, 3

2, 3

-2, -3

2, -3

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

A/x+1 + Bx+C/x²-x+1

A/x+1 – B/x²-x+1

A/x-1 – B/x²-x+1

None of these

54. Rotational fraction are of

One type

Three types

Two types

Four types

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

A/x+1 + B/(x+1)² + C/x-1

None of these

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

A/x+1 + Bx+0/x²-1

56. 1/(x – 3)(x – 2) =

1/x²-3 – 1/x-2

1/x²-3 – 1/x²-2

1/x+3 – 1/x+2

1/x-3 – 1/x-2

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

1/x²-3 – 1/x²-2

1/x-3 – 1/x-2

None of these

1/x+3 – 1/x+2

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

– 64

– 16

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

Ax+B/x+1 + C/x²-x+1

A/x+1 + Bx+C/x²-x+1

A/x+1 – B/x²-x+1

A/x-1 – B/x²-x+1

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

Identity

Equation

None of these

Algebric equation

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

Multiplication

Addition

Division

Subtraction

63. The process of partial decomposition result in

Equation

An identity

Partial fraction

None of these

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

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

3/x – 2/x+1

2/3(x-2) – 4/3(x+2)

4/3(x-4) – 1/3(x-1)

65. 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 = 2, B = 3

A = 1, B = 3

A = 4, B = 3

66. (x – 4)² = x² + 8x + 16 is

A transcendental equation

Cubic equation

An equation

An identity

67. 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

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

Equation

True Sentence

In Equation

False Sentence

69. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = x – 1, B = x + 1

A = 0, B = 2

A = x, B = 1

A = -1, B = 1

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

A proper fraction

Equation

An improper fraction

Algebraic equation

71. 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

-8, -8

-6, -10

8, 8

6, 10

72. 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)

73. 1/(x²+5)(x²+5) =

1/x²+4 – 1/x²+5

None of these

1/x²-4 – 1/x²+5

1/x²+4 – 1/x²-5

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

A/x+2 + B/(x-2)²

A/x-2 + B/(x+2)²

A/x+2 + B/x-2

None of these

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

Ax+B/x-1 + C/(x-1)² + D/(x-1)³

A/x-1 + Bx+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

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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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