Home/ECAT/ECAT Mathematics Partial Fractions Online Test

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.
Test Helpful For:	ECAT Entry Test Math Online Test Interview Questions about Math All Universities Entrance Test Recruitments Tests

ECAT Math Partial Fractions MCQS Online Test

Please wait...

Page 1 of 3

Math

1. 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

2. 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

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

1/x-3 – 1/x-2

1/x²-3 – 1/x²-2

None of these

1/x+3 – 1/x+2

4. (x – 4)² = x² – 8x + 16 is

An equation

Cubic equation

Identity equation

Transcendental Equation

5. Algebric equation can be divided into

Two kinds

Three kinds

One kind

Four kinds

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

Rational fraction

Combined fraction

None of these

Partial fraction

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

All values of x

None of these

One value of x

Two values of x

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

Equation

An improper fraction

A proper fraction

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

A = 2, B = 3

A = 1, B = 5

A = 4, B = 3

A = 1, B = 3

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

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

(Ax+B)(x²+x+1)+C(x²+x+1)²

A/x²+x+1 + B/(x²+x+1)²

None of these

11. Partial fractions of 1/x³+1 will be of the form

A/x+1 + Bx+C/x²-x+1

A/x+1 – B/x²-x+1

A/x-1 – B/x²-x+1

Ax+B/x+1 + C/x²-x+1

12. 1/(x²+x+a)(x²+x+b) =

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

1/a-b[1/x²+x+b – 1/x²+x+a]

13. 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

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

1 or -1

2 or ½

8 or 1/8

4 or ¼

15. x + 3/x = 4 is

Cubic equation

An identity

An equation

A transcendental equation

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

In equality

None of these

Equation

Fraction

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

False Sentence

In Equation

Equation

True Sentence

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

Partial fraction

None of these

Improper fraction

Combined fraction

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

A proper fraction

Equation

An improper fraction

Algebric relation

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

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

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

None of these

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

21. 4x = 5 is ?

Equation

Identity

Conditional

Fraction

22. 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)

23. (x+2)² = x² + 4x + 4 is

A linear equation

A quadratic equation

A cubic equation

None of these

24. P(x)/Q(x), Q(x) ≠ 0 is known as

Improper rational fraction

Proper rational fraction

None of these

Rational fraction

25. (x – 4)² = x² + 8x + 16 is

An equation

Cubic equation

An identity

A transcendental equation

Page 2 of 3

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

Negative

Zero

Positive

Nothing can be said

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

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

None of these

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

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

28. x²–3/3x+1 is

Proper fraction

None of these

Improper rational fraction

Rational fraction

29. 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.

(-π, 0)

(-π/2, π/2)

(0, 2 π)

(0, π)

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

“=”

≡

≠

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

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

None of these

Ax+B/(x²+2)² + C/(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

33. 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

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

Ax+B/x²-1

B/x-1

A/x+1

A/x+1 + B/x-1

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

2/3(x-2) – 4/3(x+2)

4/3(x-4) – 1/3(x-1)

3/x – 2/x+1

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

36. 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

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

Empty set

{- 3/5}

{-1}

{- 1/3}

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

Algebric relation

Algebric equation

Equation

Identity

39. Which is a proper rational fraction?

2x²–5/x²+4

None of these

2x–5/x²+4

9x⁴/x³–1

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, 5, 1)

(4, 3, 2)

(5, 3, 1)

(6, 4, 1)

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

a² + c² = – ab

a² – c² = – ab

a² – c² = ab

None of these

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

None of these

A/x-1 + B/x²+1

A/x+1 + B/x²+1

A/x+1 + Bx+C/x²+1

43. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

A = -1, B = 1

A = 0, B = 2

A = x – 1, B = x + 1

A = x, B = 1

44. 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

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

Co-efficient

Degree

Bare

Root

46. 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

47. 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

48. 2x = 3 is a conditional equation it is true for

2/3

3/2

49. x + 3/x = 4 is

An identity

Cubic equation

A transcendental equation

An equation

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

Identity

Algebric equation

Equation

None of these

Page 3 of 3

51. (x + 2)² = x² + 4x + 4 is

Cubic equation

An equation

Linear equation

An identity

52. 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

-8, -8

6, 10

53. 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)

54. 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

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

A proper fraction

Equation

An improper fraction

Algebraic equation

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

A/cx+d + bx/ex+f

None of these

A/cx+d + Bx/(ex+f)²

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

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

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

A/x+1 + Bx+0/x²-1

None of these

A/x+1 + B/(x+1)² + C/x-1

59. 9x²/x³¯¹ is a fraction.

Rational fraction

Proper fraction

None of these

Improper fraction

60. 1/(x – 3)(x – 2) =

1/x²-3 – 1/x²-2

1/x+3 – 1/x+2

1/x-3 – 1/x-2

1/x²-3 – 1/x-2

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

Algebric equation

A proper fraction

Equation

Improper fraction

62. The process of partial decomposition result in

None of these

Partial fraction

An identity

Equation

63. 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

A/x+1 – B/x²-x+1

None of these

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

A/x-2 + B/(x+2)²

A/x+2 + B/x-2

A/x+2 + B/(x-2)²

None of these

65. Rotational fraction are of

Two types

One type

Three types

Four types

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

-2, -3

-2, 3

2, -3

2, 3

67. There are _________ types of rational fraction.

Two

Five

Three

Four

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

Division

Addition

Multiplication

Subtraction

69. 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

Fraction

Algebric relation

Equation

Identity

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

3/x – 2/x+1

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

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

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

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

Algebric relation

Algebric equation

Equation

Identity

72. 2x-5/x²+4 is ___________ rational fraction

Conditional

Improper

Proper

None of these

73. (ax+b)/(cx +d)² =

A/cx+d + B/(cx+d)²

None of these

Ax+B/(cx+d)²

A/cx+d + B/cx+d

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

(1, 2)

{-1}

(-1, 2)

(-1, 1)

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

– 16

– 64

You Can Learn and Gain more Knowledge through our Online Quiz and Testing system Just Search your desired Preparation subject at Gotest.

UET Peshawar Entry Test 2025 Registration Online ETEA Test D...
ECAT Statistics Test Set 17
ECAT Statistics Test Set 16
ECAT Statistics Test Set 15
ECAT Statistics Test Set 14
ECAT Statistics Test Set 13
ECAT Statistics Test Set 12
ECAT Statistics Test Set 11
ECAT Statistics Test Set 10
ECAT Statistics Test Set 9

Maan AliLast Updated: April 18, 2025

Facebook Twitter Reddit WhatsApp Share via Email Print

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

You Might Also Like

Maan Ali

2 Comments

Leave a Reply Cancel reply

Mathematics Partial Fractions MCQS Online Test

ECAT Math Partial Fractions Chapter Online Test

ECAT Math Partial Fractions MCQS Online Test

Math

You Might Also Like

Maan Ali

Your Related

ECAT Chemistry Chemical Equilibrium Test Online

ECAT Physics Motion and Force 3 Test Online

ECAT English Sentence Completion Online Test

ECAT Chemistry Common Chemical Industries in Pakistan Test Online

ECAT Mathematics Permutations Combinations and Probability Online Test

ECAT Computer Science Fundamentals of Internet Test Online

2 Comments

Leave a Reply Cancel reply