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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. 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

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

Degree

Co-efficient

Bare

Root

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

1 or -1

2 or ½

8 or 1/8

4 or ¼

4. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = x-1, B = x + 1

A = x, B = 1

A = 0, B = 2

A = -1, B = 1

5. 1/(x – 3)(x – 2) =

1/x-3 – 1/x-2

1/x+3 – 1/x+2

1/x²-3 – 1/x²-2

1/x²-3 – 1/x-2

6. 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

7. (x – 4)² = x² + 8x + 16 is

An identity

An equation

A transcendental equation

Cubic equation

8. x + 3/x = 4 is

An equation

A transcendental equation

An identity

Cubic equation

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

Re placed factor

Reducible factor

None of these

Irreducible factor

10. 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

11. (ax+b)/(cx +d)² =

A/cx+d + B/cx+d

None of these

A/cx+d + B/(cx+d)²

Ax+B/(cx+d)²

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

-2, 3

-2, -3

2, -3

2, 3

13. 1/(x+3)(x+2) =

None of these

1/x+3 – 1/x+2

1/x²-3 – 1/x²-2

1/x-3 – 1/x-2

14. 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

15. Algebric equation can be divided into

Two kinds

Four kinds

Three kinds

One kind

16. 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

17. 4x = 5 is ?

Fraction

Equation

Conditional

Identity

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

≡

“=”

≠

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

Division

Multiplication

Subtraction

Addition

20. (x+2)² = x² + 4x + 4 is

None of these

A cubic equation

A quadratic equation

A linear equation

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

Combined fraction

None of these

Partial fraction

Improper fraction

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

Equation

A proper fraction

Algebric equation

Improper fraction

23. 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

Equation

An improper fraction

24. 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/2, π/2)

(-π, 0)

(0, 2 π)

25. (x – 4)² = x² – 8x + 16 is

Transcendental Equation

Cubic equation

An equation

Identity equation

Page 2 of 3

26. 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

(6, 4, 1)

(5, 3, 1)

(5, 5, 1)

(4, 3, 2)

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

– 64

– 16

28. 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

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

2/3(x-2) – 4/3(x+2)

3/x – 2/x+1

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

4/3(x-4) – 1/3(x-1)

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

Rational fraction

None of these

Partial fraction

Combined fraction

31. 1/(x²+x+a)(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]

1/a-b[1/x²+x+a – 1/x²+x+b]

None of these

32. 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)

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. 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

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

A proper fraction

Algebric relation

An improper fraction

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 Q(x)< degree of P(x)

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

37. (x + 2)² = x² + 4x + 4 is

Cubic equation

An identity

Linear equation

An equation

38. There are _________ types of rational fraction.

Five

Two

Three

Four

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

40. The process of partial decomposition result in

Partial fraction

Equation

An identity

None of these

41. Rotational fraction are of

One type

Two types

Four types

Three types

42. 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

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

Ax+B/(x²+2)² + C/(x+1)²

None of these

A/(x²+2)² + B/(x+1)²

Ax+B/x²+2 + Cx+D/(x²+2)² + E/x+1 + F/(x+1)²

44. 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

-8, -8

6, 10

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

Equation

Algebric relation

Algebric equation

Identity

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

In equality

None of these

Fraction

Equation

47. x + 3/x = 4 is

A transcendental equation

An equation

Cubic equation

An identity

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

Negative

Nothing can be said

Zero

Positive

49. 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)

50. 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

Rational

Non-real

Page 3 of 3

51. x²–3/3x+1 is

None of these

Proper fraction

Rational fraction

Improper rational fraction

52. 2x = 3 is a conditional equation it is true for

3/2

2/3

53. P(x)/Q(x), Q(x) ≠ 0 is known as

Proper rational fraction

Rational fraction

Improper rational fraction

None of these

54. 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)

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

A = 1, B = 3

A = 1, B = 5

A = 4, B = 3

A = 2, B = 3

56. 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}

{- 1/3}

{- 3/5}

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

a² – c² = ab

a² + c² = – ab

a² – c² = – ab

None of these

58. 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

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

Algebraic equation

An improper fraction

A proper fraction

Equation

60. 9x²/x³¯¹ is a fraction.

Proper fraction

Improper fraction

Rational fraction

None of these

61. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = 0, B = 2

A = x – 1, B = x + 1

A = -1, B = 1

A = x, B = 1

62. 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)

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

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

A/x+1 + Bx+0/x²-1

A/x+1 + B/(x+1)² + C/x-1

None of these

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

Two values of x

None of these

All values of x

One value of x

65. 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 + B/1-bx + C/1-cx

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

None of these

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

A/x-1 + B/x²+1

None of these

A/x+1 + B/x²+1

A/x+1 + Bx+C/x²+1

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

Algebric relation

Identity

Algebric equation

Equation

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

A/x-2 + B/(x+2)²

None of these

A/x+2 + B/x-2

A/x+2 + B/(x-2)²

69. 2x-5/x²+4 is ___________ rational fraction

Proper

None of these

Improper

Conditional

70. 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

71. Which is a proper rational fraction?

2x–5/x²+4

None of these

2x²–5/x²+4

9x⁴/x³–1

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

True Sentence

Equation

In Equation

False Sentence

73. 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

74. 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

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

Equation

Algebric equation

None of these

Identity

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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

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