Mathematics Partial Fractions Online Test

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You can prepare for Mathematics Partial Fractions Online Test by attempting the free online quizzes at Gotest.com.pk. We provide instant results, performance reports, and detailed explanations for every question.

Question 1

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

Answer

Nothing can be said

Question 2

2. Rotational fraction are of

Answer

Four types

Answer

Three types

Question 3

3. x + 3/x = 4 is

Answer

Cubic equation

Answer

A transcendental equation

Answer

An identity

Answer

An equation

Question 4

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

Answer

(Ax+B)(x²+x+1)+C(x²+x+1)²

Answer

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

Answer

None of these

Answer

A/x²+x+1 + B/(x²+x+1)²

Question 5

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

Answer

A/x+1 + Bx+0/x²-1

Answer

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

Answer

A/x+1 + B/(x+1)² + C/x-1

Answer

None of these

Question 6

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

Answer

Re placed factor

Answer

None of these

Answer

Irreducible factor

Answer

Reducible factor

Question 7

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

Answer

A/x+1 + Bx+C/x²+1

Answer

A/x+1 + B/x²+1

Answer

A/x-1 + B/x²+1

Answer

None of these

Question 8

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

Answer

Algebric equation

Answer

Algebric relation

Question 9

9. P(x)/Q(x), Q(x) ≠ 0 is known as

Answer

Improper rational fraction

Answer

Proper rational fraction

Answer

Rational fraction

Answer

None of these

Question 10

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

Answer

None of these

Answer

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

Answer

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

Answer

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

Question 11

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

Answer

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

Answer

3/x – 2/x+1

Answer

4/3(x-4) – 1/3(x-1)

Answer

2/3(x-2) – 4/3(x+2)

Question 12

12. 9x²/x³¯¹ is a fraction.

Answer

None of these

Answer

Rational fraction

Answer

Improper fraction

Answer

Proper fraction

Question 13

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

Answer

None of these

Answer

Algebric equation

Question 14

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

Answer

Irrational

Question 15

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

Answer

An improper fraction

Answer

A proper fraction

Answer

Algebraic equation

Question 16

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

Question 17

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

Question 18

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

Answer

Multiplication

Answer

Subtraction

Question 19

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

Answer

a² – c² = ab

Answer

a² + c² = – ab

Answer

a² – c² = – ab

Answer

None of these

Question 20

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

Answer

Rational fraction

Answer

Partial fraction

Answer

Combined fraction

Answer

None of these

Question 21

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

Answer

Algebraic equation

Answer

A proper fraction

Answer

An improper fraction

Question 22

22. 2x-5/x²+4 is ___________ rational fraction

Answer

Conditional

Answer

None of these

Question 23

23. 1/(x – 3)(x – 2) =

Answer

1/x-3 – 1/x-2

Answer

1/x²-3 – 1/x-2

Answer

1/x²-3 – 1/x²-2

Answer

1/x+3 – 1/x+2

Question 24

24. The partial fraction of 1/x²–1 is

Answer

1/2(x–1) + 1/2(x+1)

Answer

1/2(x–1) – 1/2(x+1)

Question 25

25. There are _________ types of rational fraction.

Question 26

26. 1/(x+3)(x+2) =

Answer

None of these

Answer

1/x-3 – 1/x-2

Answer

1/x²-3 – 1/x²-2

Answer

1/x+3 – 1/x+2

Question 27

27. x + 3/x = 4 is

Answer

Cubic equation

Answer

A transcendental equation

Answer

An equation

Answer

An identity

Question 28

28. (x – 4)² = x² – 8x + 16 is

Answer

Transcendental Equation

Answer

Identity equation

Answer

Cubic equation

Answer

An equation

Question 29

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.

Answer

(-π/2, π/2)

Question 30

30. 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

Question 31

31. 2x = 3 is a conditional equation it is true for

Question 32

32. If sin θ and cos θ are the roots of the equation ax² + bx + c = 0, then

Answer

(a – c)² = b² – c²

Answer

(a + c)² = b² + c²

Answer

(a – c)² = b² + c²

Answer

(a + c)² = b² – c²

Question 33

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

Answer

None of these

Answer

Partial fraction

Answer

Combined fraction

Answer

Improper fraction

Question 34

34. (x – 4)² = x² + 8x + 16 is

Answer

Cubic equation

Answer

An equation

Answer

A transcendental equation

Answer

An identity

Question 35

35. 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

Question 36

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

Answer

In equality

Answer

None of these

Question 37

37. 10x-13/(x+2)(x-9) =

Answer

3/x+2 + 7/x-9

Answer

3/x+2 – 7/x-9

Answer

3/x-2 – 7/x+9

Answer

3/x-2 + 7/x+9

Question 38

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

Answer

A = 4, B = 3

Answer

A = 1, B = 3

Answer

A = 2, B = 3

Answer

A = 1, B = 5

Question 39

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

Answer

A/x+2 + B/(x-2)²

Answer

A/x+2 + B/x-2

Answer

None of these

Answer

A/x-2 + B/(x+2)²

Question 40

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

Answer

Two values of x

Answer

One value of x

Answer

All values of x

Answer

None of these

Question 41

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

Answer

Improper fraction

Answer

Algebric equation

Answer

A proper fraction

Question 42

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

Answer

In Equation

Answer

False Sentence

Answer

True Sentence

Question 43

43. If x+p/(x-1)(x-3) = q/x-1 + 2/x-3, the value of P and Q are

Answer

P = 1, q = 1

Answer

P = 1, q = -1

Answer

P = -2, q = 1

Answer

P = 2, q = 1

Question 44

44. 1/(x²+5)(x²+5) =

Answer

1/x²+4 – 1/x²-5

Answer

None of these

Answer

1/x²+4 – 1/x²+5

Answer

1/x²-4 – 1/x²+5

Question 45

45. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

Answer

A = x-1, B = x + 1

Answer

A = 0, B = 2

Answer

A = x, B = 1

Answer

A = -1, B = 1

Question 46

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

Question 47

47. 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

Answer

Algebric relation

Question 48

48. 4x = 5 is ?

Answer

Conditional

Question 49

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

Answer

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

Answer

3/x – 2/x+1

Answer

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

Answer

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

Question 50

50. 2x²-3x+4/(x+1)³ =

Answer

2/x-1 – 7/(x-1)² + 9/(x-1)³

Answer

2/x+1 – 7/(x+1)² + 9/(x-1)³

Answer

2/x+1 – 7/(x+1)² + 9/(x+1)³

Answer

2/x-1 – 7/(x+1)² + 9/(x+1)³

Question 51

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

Answer

Algebric relation

Answer

Algebric equation

Question 52

52. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

Answer

A = 0, B = 2

Answer

A = -1, B = 1

Answer

A = x, B = 1

Answer

A = x – 1, B = x + 1

Question 53

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

Answer

A/cx+d + Bx/(ex+f)²

Answer

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

Answer

None of these

Answer

A/cx+d + bx/ex+f

Question 54

54. x/(x+2)(x–3)

Answer

2/5(x+2) – 3/5(x–3)

Answer

2/5(x+2) + 3/5(x–3)

Answer

2/5(x+2) – 3/5(x+3)

Answer

2/5(x–2) + 3/5(x+3)

Question 55

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

Question 56

56. (ax+b)/(cx +d)² =

Answer

Ax+B/(cx+d)²

Answer

A/cx+d + B/cx+d

Answer

None of these

Answer

A/cx+d + B/(cx+d)²

Question 57

57. Partial fractions of 2x²-3x+4/(x-1)³ will be of the form

Answer

A/x-1 + Bx+C/(x-1)² + D/(x-1)³

Answer

A/x+1 + B/(x+1)² + C/(x+1)³

Answer

Ax+B/x-1 + C/(x-1)² + D/(x-1)³

Answer

A/x-1 + B/(x-1)² + C/(x-1)³

Question 58

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

Answer

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

Answer

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

Answer

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

Answer

None of these

Question 59

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

Answer

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

Answer

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

Answer

None of these

Answer

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

Question 60

60. 1/(x²+x+a)(x²+x+b) =

Answer

1/a-b[1/x²+x+b – 1/x²+x+a]

Answer

1/a-b[1/x²+x+b +1/x²+x+a]

Answer

1/a-b[1/x²+x+a – 1/x²+x+b]

Answer

None of these

Question 61

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

Answer

A/x+1 – B/x²-x+1

Answer

A/x-1 – B/x²-x+1

Answer

A/x+1 + Bx+C/x²-x+1

Answer

Ax+B/x+1 + C/x²-x+1

Question 62

62. x²–3/3x+1 is

Answer

Improper rational fraction

Answer

Proper fraction

Answer

Rational fraction

Answer

None of these

Question 63

63. The process of partial decomposition result in

Answer

An identity

Answer

Partial fraction

Answer

None of these

Question 64

64. (x + 2)² = x² + 4x + 4 is

Answer

An identity

Answer

Cubic equation

Answer

Linear equation

Answer

An equation

Answer 189

An improper fraction

Answer 190

A proper fraction

Answer 191

Algebric relation

Answer 192

Three kinds

Answer 193

Four kinds

Answer 194

2x–5/x²+4

Answer 195

None of these

Answer 196

9x⁴/x³–1

Answer 197

2x²–5/x²+4

Answer 198

A/(x²+2)² + B/(x+1)²

Answer 199

None of these

Answer 200

Ax+B/(x²+2)² + C/(x+1)²

Answer 201

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

Answer 202

A/x+1 + B/x-1

Answer 203

Ax+B/x²-1

Answer 204

A quadratic equation

Answer 205

None of these

Answer 206

A cubic equation

Answer 207

A linear equation

Answer 208

Co-efficient

Answer 209

None of these

Answer 210

A/x+1 – B/x²-x+1

Answer 211

A/x-1 – B/x²-x+1

Answer 212

A/x+1 + Bx+C/x²-x+1

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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Important Math Partial Fractions Question and Answer

Math Partial Fractions Practice Test Online With Explanation

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How to Score High in Mathematics Partial Fractions Online Test?

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