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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

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Page 1 of 3

Math

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

A/(x²+2)² + B/(x+1)²

None of these

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

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

A proper fraction

An improper fraction

Algebric relation

Equation

3. 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

Identity

Equation

Algebric relation

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

Equation

None of these

Fraction

In equality

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

Improper

Conditional

Proper

None of these

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

Algebric equation

A proper fraction

Equation

Improper fraction

7. (x – 4)² = x² – 8x + 16 is

Transcendental Equation

An equation

Cubic equation

Identity equation

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

None of these

Rational fraction

Combined fraction

Partial fraction

9. The process of partial decomposition result in

None of these

Equation

An identity

Partial fraction

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

Root

Co-efficient

Bare

Degree

11. x + 3/x = 4 is

An equation

An identity

A transcendental equation

Cubic equation

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

B/x-1

Ax+B/x²-1

A/x+1

A/x+1 + B/x-1

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

-2, -3

2, 3

-2, 3

2, -3

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

2 or ½

8 or 1/8

1 or -1

4 or ¼

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

A/x+1 + B/(x+1)² + C/x-1

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

A/x+1 + Bx+0/x²-1

None of these

16. (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

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

Equation

Algebraic equation

An improper fraction

A proper fraction

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

3/x – 2/x+1

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

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

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

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

Equation

Algebric equation

Algebric relation

Identity

20. 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

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

True Sentence

In Equation

Equation

False Sentence

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

Improper fraction

None of these

Combined fraction

Partial fraction

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

A = 4, B = 3

A = 1, B = 5

A = 2, B = 3

A = 1, B = 3

24. 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

25. 1/(x – 3)(x – 2) =

1/x²-3 – 1/x-2

1/x-3 – 1/x-2

1/x+3 – 1/x+2

1/x²-3 – 1/x²-2

Page 2 of 3

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

A/x+1 + Bx+C/x²-x+1

A/x-1 – B/x²-x+1

Ax+B/x+1 + C/x²-x+1

A/x+1 – B/x²-x+1

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

a² – c² = – ab

None of these

a² – c² = ab

a² + c² = – ab

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

– 16

– 64

29. (x – 4)² = x² + 8x + 16 is

An equation

A transcendental equation

Cubic equation

An identity

30. 1/(x+3)(x+2) =

1/x-3 – 1/x-2

1/x²-3 – 1/x²-2

None of these

1/x+3 – 1/x+2

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

“=”

≡

≠

32. 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)

2/3(x-2) – 4/3(x+2)

33. 1/(x²+x+a)(x²+x+b) =

1/a-b[1/x²+x+b +1/x²+x+a]

1/a-b[1/x²+x+a – 1/x²+x+b]

None of these

1/a-b[1/x²+x+b – 1/x²+x+a]

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

35. 2x = 3 is a conditional equation it is true for

3/2

2/3

36. 4x = 5 is ?

Conditional

Fraction

Identity

Equation

37. 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

38. Which is a proper rational fraction?

None of these

2x²–5/x²+4

2x–5/x²+4

9x⁴/x³–1

39. (x + 2)² = x² + 4x + 4 is

An identity

An equation

Linear equation

Cubic equation

40. P(x)/Q(x), Q(x) ≠ 0 is known as

Proper rational fraction

Improper rational fraction

Rational fraction

None of these

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

{- 1/3}

{- 3/5}

Empty set

{-1}

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

Addition

Division

Subtraction

Multiplication

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

A/x+1 + Bx+C/x²-x+1

None of these

A/x+1 – B/x²-x+1

A/x-1 – B/x²-x+1

44. 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

45. 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, 3, 1)

(5, 5, 1)

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

A/cx+d + Bx/(ex+f)²

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

A/cx+d + bx/ex+f

None of these

47. 9x²/x³¯¹ is a fraction.

Proper fraction

Rational fraction

Improper fraction

None of these

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

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

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

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

None of these

49. Algebric equation can be divided into

One kind

Three kinds

Four kinds

Two kinds

50. 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)

Page 3 of 3

51. 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

52. 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

53. There are _________ types of rational fraction.

Three

Five

Two

Four

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

Negative

Zero

Positive

Nothing can be said

55. 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

56. 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

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

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

Algebric relation

Equation

Algebric equation

Identity

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

An improper fraction

Algebraic equation

Equation

A proper fraction

59. 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)

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

A/x-1 + B/x²+1

A/x+1 + Bx+C/x²+1

A/x+1 + B/x²+1

None of these

61. 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

Irrational

Non-real

Rational

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

(-1, 1)

{-1}

(-1, 2)

(1, 2)

63. Rotational fraction are of

Four types

Three types

One type

Two types

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

Reducible factor

None of these

Re placed factor

Irreducible factor

65. (x+2)² = x² + 4x + 4 is

A quadratic equation

None of these

A cubic equation

A linear equation

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

(Ax+B)(x²+x+1)+C(x²+x+1)²

A/x²+x+1 + B/(x²+x+1)²

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

None of these

67. 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

None of these

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

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

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

All values of x

None of these

Two values of x

One value of x

69. x²–3/3x+1 is

None of these

Proper fraction

Improper rational fraction

Rational fraction

70. 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

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

None of these

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

72. 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

73. x + 3/x = 4 is

A transcendental equation

Cubic equation

An equation

An identity

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

Algebric equation

Equation

Identity

None of these

75. 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)

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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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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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