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

None of these

a² + c² = – ab

a² – c² = – ab

a² – c² = ab

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

6, 10

8, 8

-6, -10

-8, -8

3. There are _________ types of rational fraction.

Two

Three

Four

Five

4. 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)

(-π, 0)

(-π/2, π/2)

(0, 2 π)

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

A/x+1 + Bx+C/x²-x+1

A/x+1 – B/x²-x+1

None of these

A/x-1 – B/x²-x+1

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

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

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

3/x – 2/x+1

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

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

Equation

Identity

None of these

Algebric equation

8. The process of partial decomposition result in

Equation

None of these

An identity

Partial fraction

9. (x – 4)² = x² + 8x + 16 is

A transcendental equation

An equation

Cubic equation

An identity

10. 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

Ax+B/x-1 + C/(x-1)² + D/(x-1)³

A/x+1 + B/(x+1)² + C/(x+1)³

11. 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)

12. 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)

13. 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

Algebraic equation

An improper fraction

Equation

14. 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

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

None of these

Partial fraction

Improper fraction

Combined fraction

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

Equation

A proper fraction

An improper fraction

Algebraic equation

17. 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

None of these

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

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

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

An improper fraction

Algebric relation

Equation

A proper fraction

19. 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)

20. 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

21. 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

22. 2x = 3 is a conditional equation it is true for

2/3

3/2

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

Equation

False Sentence

In Equation

True Sentence

24. 1/(x+3)(x+2) =

None of these

1/x+3 – 1/x+2

1/x-3 – 1/x-2

1/x²-3 – 1/x²-2

25. 4x = 5 is ?

Fraction

Equation

Conditional

Identity

Page 2 of 3

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

None of these

A/x+2 + B/(x-2)²

A/x-2 + B/(x+2)²

A/x+2 + B/x-2

27. 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

28. 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

Fraction

Identity

Equation

29. 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

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

≡

≠

“=”

31. x + 3/x = 4 is

Cubic equation

An identity

An equation

A transcendental equation

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

Identity

Algebric relation

Equation

Algebric equation

33. 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

34. (x + 2)² = x² + 4x + 4 is

Cubic equation

An equation

Linear equation

An identity

35. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = x, B = 1

A = -1, B = 1

A = 0, B = 2

A = x-1, B = x + 1

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

Equation

None of these

Fraction

In equality

37. 1/(x – 3)(x – 2) =

1/x²-3 – 1/x²-2

1/x²-3 – 1/x-2

1/x+3 – 1/x+2

1/x-3 – 1/x-2

38. 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

39. P(x)/Q(x), Q(x) ≠ 0 is known as

None of these

Rational fraction

Improper rational fraction

Proper rational fraction

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

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

– 64

– 16

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

Division

Multiplication

Subtraction

Addition

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

Negative

Positive

Zero

44. 9x²/x³¯¹ is a fraction.

Proper fraction

Rational fraction

None of these

Improper fraction

45. (ax+b)/(cx +d)² =

Ax+B/(cx+d)²

A/cx+d + B/cx+d

None of these

A/cx+d + B/(cx+d)²

46. (x+2)² = x² + 4x + 4 is

A quadratic equation

None of these

A cubic equation

A linear equation

47. Algebric equation can be divided into

Three kinds

One kind

Four kinds

Two kinds

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

Rational fraction

Partial fraction

None of these

Combined fraction

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

A/x+1 + B/x-1

Ax+B/x²-1

A/x+1

B/x-1

50. Rotational fraction are of

Three types

One type

Four types

Two types

Page 3 of 3

51. Which is a proper rational fraction?

None of these

2x–5/x²+4

2x²–5/x²+4

9x⁴/x³–1

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

Bare

Co-efficient

Root

Degree

53. 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

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

(Ax+B)(x²+x+1)+C(x²+x+1)²

None of these

A/x²+x+1 + B/(x²+x+1)²

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

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

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

3/x – 2/x+1

4/3(x-4) – 1/3(x-1)

2/3(x-2) – 4/3(x+2)

56. 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

57. 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

58. (x – 4)² = x² – 8x + 16 is

An equation

Identity equation

Cubic equation

Transcendental Equation

59. 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)

(5, 3, 1)

(6, 4, 1)

(5, 5, 1)

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

None of these

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

A/x+1 + B/(x+1)² + C/x-1

A/x+1 + Bx+0/x²-1

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

Algebric equation

Identity

Equation

Algebric relation

62. 1/(x²+x+a)(x²+x+b) =

1/a-b[1/x²+x+b +1/x²+x+a]

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]

63. The partial fraction of 1/x²–1 is

1/2(x+1)

1/(x–1)

1/2(x–1) + 1/2(x+1)

1/2(x–1) – 1/2(x+1)

64. x + 3/x = 4 is

A transcendental equation

Cubic equation

An identity

An equation

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

-2, -3

2, 3

-2, 3

2, -3

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

Non-real

Irrational

Zero

Rational

67. 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

68. 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

69. x²–3/3x+1 is

Proper fraction

Rational fraction

Improper rational fraction

None of these

70. 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

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

2 or ½

4 or ¼

1 or -1

8 or 1/8

72. 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}

73. 2x-5/x²+4 is ___________ rational fraction

Conditional

None of these

Improper

Proper

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

Two values of x

One value of x

All values of x

None of these

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

None of these

Irreducible factor

Re placed factor

Reducible factor

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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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