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

Conditional

Improper

Proper

None of these

2. 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

6, 10

-8, -8

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

2/3(x-2) – 4/3(x+2)

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

4/3(x-4) – 1/3(x-1)

3/x – 2/x+1

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

Reducible factor

Re placed factor

Irreducible factor

None of these

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

2, -3

2, 3

-2, -3

-2, 3

6. 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)

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

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

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

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

None of these

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

Algebric equation

Algebric relation

Identity

Equation

9. 2x = 3 is a conditional equation it is true for

3/2

2/3

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

2 or ½

4 or ¼

1 or -1

8 or 1/8

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

A proper fraction

An improper fraction

Equation

Algebric relation

12. 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 – B/x²-x+1

A/x+1 + Bx+C/x²-x+1

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

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

None of these

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

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

14. 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

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

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

False Sentence

True Sentence

In Equation

Equation

16. 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

None of these

Ax+B/(x²+2)² + C/(x+1)²

17. 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

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

Improper fraction

Algebric equation

Equation

A proper fraction

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

A/x+1 + Bx+C/x²+1

None of these

A/x-1 + B/x²+1

A/x+1 + B/x²+1

20. 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

Rational

Irrational

Non-real

21. Which is a proper rational fraction?

2x–5/x²+4

9x⁴/x³–1

None of these

2x²–5/x²+4

22. Rotational fraction are of

Two types

Three types

One type

Four types

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

a² + c² = – ab

a² – c² = ab

None of these

a² – c² = – ab

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

A/x+1 + Bx+0/x²-1

None of these

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

A/x+1 + B/(x+1)² + C/x-1

25. (x+2)² = x² + 4x + 4 is

A quadratic equation

A linear equation

A cubic equation

None of these

Page 2 of 3

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

Equation

None of these

Algebric equation

Identity

27. x²–3/3x+1 is

Improper rational fraction

Proper fraction

Rational fraction

None of these

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

Identity

Equation

Algebric equation

Algebric relation

29. 1/(x²+5)(x²+5) =

None of these

1/x²+4 – 1/x²+5

1/x²+4 – 1/x²-5

1/x²-4 – 1/x²+5

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

A/x-1 – B/x²-x+1

A/x+1 + Bx+C/x²-x+1

A/x+1 – B/x²-x+1

None of these

31. 4x = 5 is ?

Identity

Fraction

Equation

Conditional

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

Equation

In equality

Fraction

None of these

33. 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

Equation

A proper fraction

Algebraic equation

34. 9x²/x³¯¹ is a fraction.

Rational fraction

Proper fraction

Improper fraction

None of these

35. x + 3/x = 4 is

A transcendental equation

An identity

Cubic equation

An equation

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

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

None of these

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

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

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

≠

≡

“=”

38. 1/(x²+x+a)(x²+x+b) =

None of these

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]

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

None of these

Partial fraction

Combined fraction

Rational fraction

40. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = 0, B = 2

A = x – 1, B = x + 1

A = x, B = 1

A = -1, B = 1

41. There are _________ types of rational fraction.

Four

Two

Three

Five

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

Algebraic equation

Equation

A proper fraction

An improper fraction

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

Nothing can be said

Zero

Positive

Negative

44. 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

45. 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

46. 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 = 2, B = 3

A = 1, B = 5

A = 1, B = 3

47. (x – 4)² = x² + 8x + 16 is

An identity

Cubic equation

An equation

A transcendental equation

48. 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

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

One value of x

Two values of x

None of these

All values of x

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

A/cx+d + bx/ex+f

A/cx+d + Bx/(ex+f)²

None of these

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

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. (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

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

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

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

A/x²+x+1 + B/(x²+x+1)²

None of these

(Ax+B)(x²+x+1)+C(x²+x+1)²

55. x + 3/x = 4 is

A transcendental equation

An equation

Cubic equation

An identity

56. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = -1, B = 1

A = x, B = 1

A = x-1, B = x + 1

A = 0, B = 2

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

Addition

Multiplication

Division

Subtraction

58. P(x)/Q(x), Q(x) ≠ 0 is known as

Improper rational fraction

Rational fraction

Proper rational fraction

None of these

59. 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)

(0, 2 π)

(-π, 0)

(-π/2, π/2)

60. (x – 4)² = x² – 8x + 16 is

Identity equation

Cubic equation

An equation

Transcendental Equation

61. 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}

{-1}

Empty set

62. 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)

63. 1/(x – 3)(x – 2) =

1/x+3 – 1/x+2

1/x²-3 – 1/x²-2

1/x²-3 – 1/x-2

1/x-3 – 1/x-2

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

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

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

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

3/x – 2/x+1

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

Partial fraction

Improper fraction

None of these

Combined fraction

66. 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

67. The process of partial decomposition result in

Equation

Partial fraction

An identity

None of these

68. (x + 2)² = x² + 4x + 4 is

An equation

An identity

Linear equation

Cubic equation

69. 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)

(6, 4, 1)

(5, 5, 1)

(4, 3, 2)

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

– 64

– 16

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

Ax+B/x²-1

A/x+1 + B/x-1

B/x-1

A/x+1

72. 1/(x+3)(x+2) =

1/x+3 – 1/x+2

1/x-3 – 1/x-2

None of these

1/x²-3 – 1/x²-2

73. Algebric equation can be divided into

One kind

Three kinds

Four kinds

Two kinds

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

{-1}

(1, 2)

(-1, 2)

(-1, 1)

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

Degree

Bare

Root

Co-efficient

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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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