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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. 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)

2. 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)

3. (ax+b)/(cx +d)² =

A/cx+d + B/cx+d

Ax+B/(cx+d)²

None of these

A/cx+d + B/(cx+d)²

4. 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

Equation

Fraction

Algebric relation

Identity

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

Equation

An improper fraction

Algebraic equation

A proper fraction

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

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

(Ax+B)(x²+x+1)+C(x²+x+1)²

None of these

A/x²+x+1 + B/(x²+x+1)²

7. There are _________ types of rational fraction.

Two

Four

Three

Five

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

Irrational

Non-real

Zero

Rational

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

None of these

Algebric equation

Identity

Equation

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

A/x+1 + Bx+C/x²+1

A/x-1 + B/x²+1

A/x+1 + B/x²+1

None of these

11. 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]

1/a-b[1/x²+x+b +1/x²+x+a]

None of these

12. 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 + B/(x+1)² + C/(x+1)³

Ax+B/x-1 + C/(x-1)² + D/(x-1)³

A/x-1 + Bx+C/(x-1)² + D/(x-1)³

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

None of these

A/x-1 – B/x²-x+1

A/x+1 + Bx+C/x²-x+1

A/x+1 – B/x²-x+1

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

A/x+1 + B/x-1

B/x-1

A/x+1

Ax+B/x²-1

15. 4x = 5 is ?

Fraction

Equation

Identity

Conditional

16. x²–3/3x+1 is

Rational fraction

Improper rational fraction

Proper fraction

None of these

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

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

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

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

3/x – 2/x+1

18. The partial fraction of 1/x²–1 is

1/2(x+1)

1/2(x–1) + 1/2(x+1)

1/(x–1)

1/2(x–1) – 1/2(x+1)

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

None of these

In equality

Fraction

Equation

20. 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

None of these

A/x+2 + B/x-2

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

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

None of these

A/x+1 + Bx+0/x²-1

A/x+1 + B/(x+1)² + C/x-1

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

-2, -3

2, -3

-2, 3

2, 3

23. 9x²/x³¯¹ is a fraction.

None of these

Proper fraction

Improper fraction

Rational fraction

24. x + 3/x = 4 is

A transcendental equation

Cubic equation

An identity

An equation

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

Algebric relation

Equation

Identity

Algebric equation

Page 2 of 3

26. (x + 2)² = x² + 4x + 4 is

An equation

Linear equation

Cubic equation

An identity

27. 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)

(4, 3, 2)

(6, 4, 1)

(5, 5, 1)

28. x + 3/x = 4 is

An identity

Cubic equation

An equation

A transcendental equation

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

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

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

None of these

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

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

Co-efficient

Root

Bare

Degree

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

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

None of these

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

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

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

None of these

Improper fraction

Partial fraction

Combined fraction

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

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

One value of x

None of these

All values of x

Two values of x

35. 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

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

A proper fraction

Algebric equation

Equation

Improper fraction

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

Equation

Algebric relation

Identity

Algebric equation

38. P(x)/Q(x), Q(x) ≠ 0 is known as

None of these

Proper rational fraction

Improper rational fraction

Rational fraction

39. 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

{- 1/3}

{-1}

40. 2x = 3 is a conditional equation it is true for

3/2

2/3

41. (x – 4)² = x² – 8x + 16 is

Identity equation

Cubic equation

Transcendental Equation

An equation

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

A proper fraction

Algebraic equation

An improper fraction

Equation

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

A/x+1 + Bx+C/x²-x+1

Ax+B/x+1 + C/x²-x+1

A/x-1 – B/x²-x+1

A/x+1 – B/x²-x+1

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

Multiplication

Division

Subtraction

Addition

45. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = x – 1, B = x + 1

A = -1, B = 1

A = 0, B = 2

A = x, B = 1

46. 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

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

{-1}

(1, 2)

(-1, 1)

(-1, 2)

48. 1/(x – 3)(x – 2) =

1/x²-3 – 1/x²-2

1/x+3 – 1/x+2

1/x-3 – 1/x-2

1/x²-3 – 1/x-2

49. 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

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

Combined fraction

Partial fraction

Rational fraction

None of these

Page 3 of 3

51. 2x-5/x²+4 is ___________ rational fraction

Improper

None of these

Proper

Conditional

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

Algebric relation

A proper fraction

Equation

An improper fraction

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

– 64

– 16

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

4 or ¼

2 or ½

8 or 1/8

1 or -1

55. Which is a proper rational fraction?

2x–5/x²+4

2x²–5/x²+4

None of these

9x⁴/x³–1

56. 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

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

≠

“=”

≡

58. (x+2)² = x² + 4x + 4 is

A quadratic equation

None of these

A cubic equation

A linear equation

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

None of these

a² – c² = ab

a² + c² = – ab

a² – c² = – ab

60. 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)

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

In Equation

Equation

True Sentence

False Sentence

62. 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

63. 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 = 1, B = 5

A = 4, B = 3

64. 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

A/(x²+2)² + B/(x+1)²

Ax+B/(x²+2)² + C/(x+1)²

None of these

65. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = x-1, B = x + 1

A = x, B = 1

A = -1, B = 1

A = 0, B = 2

66. Algebric equation can be divided into

Four kinds

Two kinds

One kind

Three kinds

67. 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

6, 10

-8, -8

68. The process of partial decomposition result in

Partial fraction

None of these

Equation

An identity

69. 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 = -2, q = 1

P = 1, q = -1

P = 1, q = 1

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

Irreducible factor

Re placed factor

None of these

Reducible factor

71. 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

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

None of these

72. Rotational fraction are of

Four types

Two types

One type

Three types

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

A/cx+d + bx/ex+f

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

A/cx+d + Bx/(ex+f)²

None of these

74. (x – 4)² = x² + 8x + 16 is

Cubic equation

A transcendental equation

An equation

An identity

75. 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

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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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