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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 x²+1/x²+1 will be of the form

A/x-1 – B/x²-x+1

A/x+1 – B/x²-x+1

A/x+1 + Bx+C/x²-x+1

None of these

2. 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

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

Identity

Equation

Algebric equation

Algebric relation

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

An improper fraction

A proper fraction

Algebric relation

Equation

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

Combined fraction

Partial fraction

None of these

Improper fraction

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

– 64

– 16

7. 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

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

Algebraic equation

An improper fraction

Equation

A proper fraction

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

Positive

Zero

Nothing can be said

Negative

10. There are _________ types of rational fraction.

Five

Three

Two

Four

11. 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

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

Equation

False Sentence

True Sentence

In Equation

13. x + 3/x = 4 is

An equation

A transcendental equation

Cubic equation

An identity

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

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

4/3(x-4) – 1/3(x-1)

3/x – 2/x+1

2/3(x-2) – 4/3(x+2)

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

Rational fraction

Partial fraction

None of these

Combined fraction

16. 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

Identity

Fraction

Equation

Algebric relation

17. 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

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

Addition

Multiplication

Division

Subtraction

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

All values of x

One value of x

Two values of x

None of these

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

≠

“=”

≡

21. 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)

22. 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]

1/a-b[1/x²+x+b +1/x²+x+a]

None of these

23. Rotational fraction are of

Four types

Two types

Three types

One type

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

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

None of these

25. x + 3/x = 4 is

Cubic equation

An identity

A transcendental equation

An equation

Page 2 of 3

26. (ax+b)/(cx +d)² =

None of these

A/cx+d + B/(cx+d)²

Ax+B/(cx+d)²

A/cx+d + B/cx+d

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

Identity

Algebric equation

Equation

Algebric relation

28. (x – 4)² = x² + 8x + 16 is

An identity

A transcendental equation

An equation

Cubic equation

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

{- 3/5}

{- 1/3}

{-1}

Empty set

30. 9x²/x³¯¹ is a fraction.

Rational fraction

Improper fraction

None of these

Proper fraction

31. (x + 2)² = x² + 4x + 4 is

Linear equation

An identity

An equation

Cubic equation

32. 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

33. 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

34. 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

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

a² – c² = ab

a² + c² = – ab

None of these

a² – c² = – ab

36. 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

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

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

Fraction

In equality

None of these

Equation

39. 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

6, 10

-8, -8

8, 8

40. 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)

(4, 3, 2)

(5, 5, 1)

41. 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

42. 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

43. 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

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

A/x-2 + B/(x+2)²

A/x+2 + B/x-2

None of these

A/x+2 + B/(x-2)²

45. 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)

46. 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

47. The partial fraction of 1/x²–1 is

1/2(x–1) – 1/2(x+1)

1/2(x–1) + 1/2(x+1)

1/2(x+1)

1/(x–1)

48. 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

49. 2x-5/x²+4 is ___________ rational fraction

Conditional

None of these

Proper

Improper

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

Algebric equation

Equation

Identity

None of these

Page 3 of 3

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

(Ax+B)(x²+x+1)+C(x²+x+1)²

None of these

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

A/x²+x+1 + B/(x²+x+1)²

52. The process of partial decomposition result in

Partial fraction

None of these

An identity

Equation

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

2, -3

2, 3

-2, -3

-2, 3

54. 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 = -2, q = 1

P = 2, q = 1

P = 1, q = -1

55. 2x = 3 is a conditional equation it is true for

2/3

3/2

56. (x+2)² = x² + 4x + 4 is

A linear equation

None of these

A cubic equation

A quadratic equation

57. P(x)/Q(x), Q(x) ≠ 0 is known as

Rational fraction

Proper rational fraction

None of these

Improper rational fraction

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

Bare

Co-efficient

Degree

Root

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

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

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

3/x – 2/x+1

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

60. 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 = 4, B = 3

A = 2, B = 3

A = 1, B = 3

61. 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

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

None of these

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

62. 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

63. 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 Q(x)< degree of P(x)

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

64. Which is a proper rational fraction?

9x⁴/x³–1

None of these

2x–5/x²+4

2x²–5/x²+4

65. 1/(x+3)(x+2) =

1/x-3 – 1/x-2

None of these

1/x²-3 – 1/x²-2

1/x+3 – 1/x+2

66. x²–3/3x+1 is

Proper fraction

None of these

Improper rational fraction

Rational fraction

67. 4x = 5 is ?

Fraction

Identity

Conditional

Equation

68. (x – 4)² = x² – 8x + 16 is

Transcendental Equation

An equation

Cubic equation

Identity equation

69. 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

70. 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

71. Algebric equation can be divided into

One kind

Four kinds

Three kinds

Two kinds

72. 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

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

Algebraic equation

An improper fraction

Equation

A proper fraction

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

1 or -1

8 or 1/8

2 or ½

4 or ¼

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

(1, 2)

{-1}

(-1, 1)

(-1, 2)

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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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