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ECAT Mathematics Partial Fractions Online Test

Maan AliLast Updated: April 18, 2025

Mathematics Partial Fractions MCQS Online Test

ECAT Math Partial Fractions Chapter Online Test

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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ECAT Math Partial Fractions MCQS Online Test

Page 1 of 3

Math

1. 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

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

Equation

A proper fraction

Improper fraction

Algebric equation

3. (x + 2)² = x² + 4x + 4 is

An equation

Cubic equation

Linear equation

An identity

4. 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

5. x + 3/x = 4 is

Cubic equation

A transcendental equation

An identity

An equation

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

7. (x – 4)² = x² + 8x + 16 is

An equation

An identity

Cubic equation

A transcendental equation

8. 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)

9. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = x-1, B = x + 1

A = -1, B = 1

A = x, B = 1

A = 0, B = 2

10. 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

Fraction

Algebric relation

Identity

Equation

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

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

A/cx+d + Bx/(ex+f)²

A/cx+d + bx/ex+f

None of these

12. 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)

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

a² – c² = ab

None of these

a² – c² = – ab

a² + c² = – ab

14. 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, 5, 1)

(5, 3, 1)

(6, 4, 1)

(4, 3, 2)

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

A/x²+x+1 + B/(x²+x+1)²

None of these

(Ax+B)(x²+x+1)+C(x²+x+1)²

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

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

Algebric equation

Identity

Algebric relation

Equation

17. 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

18. P(x)/Q(x), Q(x) ≠ 0 is known as

Improper rational fraction

None of these

Rational fraction

Proper rational fraction

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

Algebric relation

Equation

A proper fraction

An improper fraction

20. Rotational fraction are of

One type

Two types

Four types

Three types

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

Irreducible factor

Reducible factor

None of these

Re placed factor

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

Root

Bare

Co-efficient

Degree

23. 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)

None of these

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

24. 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

25. 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

Page 2 of 3

26. 1/(x+3)(x+2) =

1/x+3 – 1/x+2

1/x²-3 – 1/x²-2

1/x-3 – 1/x-2

None of these

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

None of these

Equation

Algebric equation

Identity

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

≡

“=”

≠

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

Addition

Division

Subtraction

Multiplication

30. 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

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

Algebric equation

Equation

Algebric relation

Identity

32. 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

33. (x – 4)² = x² – 8x + 16 is

Transcendental Equation

Cubic equation

Identity equation

An equation

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

All values of x

Two values of x

One value of x

None of these

35. 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}

36. 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]

37. Which is a proper rational fraction?

2x–5/x²+4

2x²–5/x²+4

9x⁴/x³–1

None of these

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

Zero

Nothing can be said

Positive

Negative

39. (ax+b)/(cx +d)² =

A/cx+d + B/(cx+d)²

A/cx+d + B/cx+d

Ax+B/(cx+d)²

None of these

40. 1/(x – 3)(x – 2) =

1/x²-3 – 1/x-2

1/x-3 – 1/x-2

1/x²-3 – 1/x²-2

1/x+3 – 1/x+2

41. (x+2)² = x² + 4x + 4 is

A quadratic equation

A linear equation

A cubic equation

None of these

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

(-1, 2)

{-1}

(1, 2)

(-1, 1)

43. 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 = 1, q = -1

P = 2, q = 1

P = -2, q = 1

44. 9x²/x³¯¹ is a fraction.

Improper fraction

None of these

Proper fraction

Rational fraction

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

2, 3

-2, -3

-2, 3

2, -3

46. 1/(x²+5)(x²+5) =

1/x²+4 – 1/x²+5

1/x²-4 – 1/x²+5

1/x²+4 – 1/x²-5

None of these

47. 4x = 5 is ?

Fraction

Conditional

Identity

Equation

48. 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 + B/(x-1)² + C/(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

49. 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

Non-real

Irrational

Zero

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

In Equation

False Sentence

True Sentence

Equation

Page 3 of 3

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

Improper fraction

None of these

Partial fraction

Combined fraction

52. 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

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

1 or -1

2 or ½

8 or 1/8

4 or ¼

54. 2x-5/x²+4 is ___________ rational fraction

Improper

Proper

Conditional

None of these

55. 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/2, π/2)

(0, π)

(-π, 0)

56. 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

57. Algebric equation can be divided into

One kind

Three kinds

Two kinds

Four kinds

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

– 64

– 16

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

A/x-1 – B/x²-x+1

A/x+1 – B/x²-x+1

None of these

A/x+1 + Bx+C/x²-x+1

60. x²–3/3x+1 is

Rational fraction

Improper rational fraction

Proper fraction

None of these

61. There are _________ types of rational fraction.

Two

Five

Four

Three

62. 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

-8, -8

6, 10

-6, -10

63. 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

64. The process of partial decomposition result in

None of these

Equation

An identity

Partial fraction

65. x + 3/x = 4 is

Cubic equation

An equation

An identity

A transcendental equation

66. 2x = 3 is a conditional equation it is true for

3/2

2/3

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

Ax+B/x²-1

A/x+1 + B/x-1

A/x+1

B/x-1

68. 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

A/(x²+2)² + B/(x+1)²

None of these

69. 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

70. 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

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

None of these

Combined fraction

Rational fraction

Partial fraction

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

None of these

A/x-1 + B/x²+1

A/x+1 + Bx+C/x²+1

A/x+1 + B/x²+1

73. 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 + Bx+C/1-bx + D/1-cx

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

None of these

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

Fraction

Equation

None of these

In equality

75. 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 = 2, B = 3

A = 4, B = 3

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Maan AliLast Updated: April 18, 2025

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ECAT Mathematics Partial Fractions Online Test

Mathematics Partial Fractions MCQS Online Test

ECAT Math Partial Fractions Chapter Online Test

ECAT Math Partial Fractions MCQS Online Test

Math

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Maan Ali

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Mathematics Partial Fractions MCQS Online Test

ECAT Math Partial Fractions Chapter Online Test

ECAT Math Partial Fractions MCQS Online Test

Math

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Maan Ali

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