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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. (x+2)² = x² + 4x + 4 is

A linear equation

None of these

A cubic equation

A quadratic equation

2. Algebric equation can be divided into

Two kinds

One kind

Four kinds

Three kinds

3. 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

4. 1/(x²+5)(x²+5) =

1/x²+4 – 1/x²+5

1/x²+4 – 1/x²-5

None of these

1/x²-4 – 1/x²+5

5. 1/(x+3)(x+2) =

None of these

1/x²-3 – 1/x²-2

1/x+3 – 1/x+2

1/x-3 – 1/x-2

6. 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

7. 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, 2)

{-1}

8. The process of partial decomposition result in

None of these

Partial fraction

Equation

An identity

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

“=”

≠

≡

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

None of these

Reducible factor

Irreducible factor

Re placed factor

11. 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

12. (x – 4)² = x² + 8x + 16 is

A transcendental equation

Cubic equation

An equation

An identity

13. 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]

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

None of these

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

15. 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)

(0, 2 π)

(-π, 0)

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

Equation

Algebric equation

Identity

Algebric relation

17. 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)

18. 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

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

Improper fraction

Algebric equation

A proper fraction

Equation

20. (x – 4)² = x² – 8x + 16 is

An equation

Identity equation

Cubic equation

Transcendental Equation

21. (ax+b)/(cx +d)² =

A/cx+d + B/(cx+d)²

Ax+B/(cx+d)²

None of these

A/cx+d + B/cx+d

22. 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

Zero

Irrational

Rational

23. 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

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

None of these

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

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

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

25. 2x-5/x²+4 is ___________ rational fraction

Improper

None of these

Conditional

Proper

Page 2 of 3

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

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

A/cx+d + bx/ex+f

None of these

A/cx+d + Bx/(ex+f)²

27. (x + 2)² = x² + 4x + 4 is

Cubic equation

An equation

Linear equation

An identity

28. P(x)/Q(x), Q(x) ≠ 0 is known as

Rational fraction

Proper rational fraction

Improper rational fraction

None of these

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

Empty set

{- 1/3}

{-1}

{- 3/5}

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

2/3(x-2) – 4/3(x+2)

4/3(x-4) – 1/3(x-1)

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

3/x – 2/x+1

31. 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

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

-2, 3

2, -3

-2, -3

2, 3

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

An improper fraction

A proper fraction

Algebric relation

Equation

34. Partial fractions of 1/x³+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

Ax+B/x+1 + C/x²-x+1

35. Which is a proper rational fraction?

9x⁴/x³–1

None of these

2x²–5/x²+4

2x–5/x²+4

36. 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

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

None of these

A/x+1 + Bx+C/x²+1

A/x+1 + B/x²+1

A/x-1 + B/x²+1

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

Equation

An improper fraction

Algebraic equation

A proper fraction

39. 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

Equation

Identity

40. 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

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

Ax+B/(x²+2)² + C/(x+1)²

None of these

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

A/(x²+2)² + B/(x+1)²

42. 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 = 3

A = 1, B = 5

43. 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

44. 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

None of these

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

45. 9x²/x³¯¹ is a fraction.

Improper fraction

None of these

Proper fraction

Rational fraction

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

Equation

In Equation

True Sentence

False Sentence

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

Positive

Negative

Zero

Nothing can be said

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

Combined fraction

Improper fraction

None of these

Partial fraction

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

A/x+1

A/x+1 + B/x-1

B/x-1

Ax+B/x²-1

50. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = 0, B = 2

A = -1, B = 1

A = x – 1, B = x + 1

A = x, B = 1

Page 3 of 3

51. 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)

(5, 5, 1)

(6, 4, 1)

(4, 3, 2)

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

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

Fraction

Equation

In equality

None of these

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

3/x – 2/x+1

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

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

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

55. Rotational fraction are of

Three types

Four types

Two types

One type

56. 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

57. x + 3/x = 4 is

An identity

Cubic equation

A transcendental equation

An equation

58. x + 3/x = 4 is

An equation

An identity

A transcendental equation

Cubic equation

59. 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

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

None of these

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

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

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

61. x²–3/3x+1 is

None of these

Proper fraction

Improper rational fraction

Rational fraction

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

1 or -1

2 or ½

8 or 1/8

4 or ¼

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

– 16

– 64

64. 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

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

None of these

Equation

Identity

Algebric equation

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

Root

Co-efficient

Bare

Degree

67. There are _________ types of rational fraction.

Two

Five

Three

Four

68. 2x = 3 is a conditional equation it is true for

2/3

3/2

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

Algebric equation

Algebric relation

Identity

Equation

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

None of these

a² – c² = – ab

a² – c² = ab

a² + c² = – ab

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

Subtraction

Multiplication

Addition

Division

72. 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)

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

Partial fraction

None of these

Combined fraction

Rational fraction

74. 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

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 + B/(x+1)² + C/(x+1)³

75. 4x = 5 is ?

Identity

Fraction

Conditional

Equation

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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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