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

Answer

3/x – 2/x+1

Answer

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

Answer

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

Answer

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

Question 2

2. x + 3/x = 4 is

Answer

Cubic equation

Answer

An equation

Answer

An identity

Answer

A transcendental equation

Question 3

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

Question 4

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

Question 5

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

Answer

A/x+1 + B/x-1

Answer

Ax+B/x²-1

Question 6

6. There are _________ types of rational fraction.

Question 7

7. Rotational fraction are of

Answer

Three types

Answer

Four types

Question 8

8. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

Answer

A = -1, B = 1

Answer

A = x, B = 1

Answer

A = x – 1, B = x + 1

Answer

A = 0, B = 2

Question 9

9. 1/(x+3)(x+2) =

Answer

1/x-3 – 1/x-2

Answer

1/x+3 – 1/x+2

Answer

1/x²-3 – 1/x²-2

Answer

None of these

Question 10

10. 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 = 2, q = 1

Answer

P = -2, q = 1

Answer

P = 1, q = 1

Question 11

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

Answer

4/3(x-4) – 1/3(x-1)

Answer

3/x – 2/x+1

Answer

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

Answer

2/3(x-2) – 4/3(x+2)

Question 12

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

Answer

Co-efficient

Question 13

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

Question 14

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

Question 15

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

Answer

Combined fraction

Answer

Partial fraction

Answer

None of these

Answer

Improper fraction

Question 16

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

Answer

One value of x

Answer

All values of x

Answer

Two values of x

Answer

None of these

Question 17

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

Answer

a² – c² = – ab

Answer

a² – c² = ab

Answer

None of these

Answer

a² + c² = – ab

Question 18

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

Answer

None of these

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

Question 19

19. 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 20

20. 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 21

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

Question 22

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

Answer

In Equation

Answer

True Sentence

Answer

False Sentence

Question 23

23. 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 24

24. 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 25

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

Answer

A/x-1 + B/x²+1

Answer

None of these

Answer

A/x+1 + B/x²+1

Answer

A/x+1 + Bx+C/x²+1

Question 26

26. x + 3/x = 4 is

Answer

Cubic equation

Answer

A transcendental equation

Answer

An equation

Answer

An identity

Question 27

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

Answer

Multiplication

Answer

Subtraction

Question 28

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

Answer

Algebric relation

Answer

Algebric equation

Question 29

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

Answer

Partial fraction

Answer

Rational fraction

Answer

Combined fraction

Answer

None of these

Question 30

30. 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 31

31. Which is a proper rational fraction?

Answer

2x²–5/x²+4

Answer

9x⁴/x³–1

Answer

None of these

Answer

2x–5/x²+4

Question 32

32. 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 33

33. 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 34

34. (x+2)² = x² + 4x + 4 is

Answer

A cubic equation

Answer

None of these

Answer

A linear equation

Answer

A quadratic equation

Question 35

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

Answer

A/x+1 + Bx+0/x²-1

Answer

A/x+1 + B/(x+1)² + C/x-1

Answer

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

Answer

None of these

Question 36

36. 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-1, B = x + 1

Answer

A = x, B = 1

Question 37

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

Answer

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

Answer

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

Answer

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

Answer

None of these

Question 38

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

Answer

A proper fraction

Answer

An improper fraction

Answer

Algebraic equation

Question 39

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

Answer

A proper fraction

Answer

Algebraic equation

Answer

An improper fraction

Question 40

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

Answer

A/cx+d + Bx/(ex+f)²

Answer

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

Answer

A/cx+d + bx/ex+f

Answer

None of these

Question 41

41. 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 42

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

Question 43

43. 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

None of these

Answer

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

Answer

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

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. x²–3/3x+1 is

Answer

None of these

Answer

Proper fraction

Answer

Rational fraction

Answer

Improper rational fraction

Question 46

46. 4x = 5 is ?

Answer

Conditional

Question 47

47. 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 48

48. (x – 4)² = x² + 8x + 16 is

Answer

An identity

Answer

A transcendental equation

Answer

Cubic equation

Answer

An equation

Question 49

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

Answer

A proper fraction

Answer

Improper fraction

Answer

Algebric equation

Question 50

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

Answer

A = 1, B = 5

Answer

A = 1, B = 3

Answer

A = 2, B = 3

Answer

A = 4, B = 3

Question 51

51. (ax+b)/(cx +d)² =

Answer

None of these

Answer

A/cx+d + B/(cx+d)²

Answer

Ax+B/(cx+d)²

Answer

A/cx+d + B/cx+d

Question 52

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

Answer

In equality

Answer

None of these

Question 53

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

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

Answer

A/x-1 + B/(x-1)² + C/(x-1)³

Answer

A/x-1 + Bx+C/(x-1)² + D/(x-1)³

Question 54

54. 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 55

55. 2x = 3 is a conditional equation it is true for

Question 56

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

Answer

An improper fraction

Answer

A proper fraction

Answer

Algebric relation

Question 57

57. 2x-5/x²+4 is ___________ rational fraction

Answer

Conditional

Answer

None of these

Question 58

58. 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 59

59. The process of partial decomposition result in

Answer

None of these

Answer

An identity

Answer

Partial fraction

Question 60

60. 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 61

61. 1/(x – 3)(x – 2) =

Answer

1/x-3 – 1/x-2

Answer

1/x²-3 – 1/x-2

Answer

1/x+3 – 1/x+2

Answer

1/x²-3 – 1/x²-2

Question 62

62. 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 63

63. 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 64

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

Answer

A/x+2 + B/x-2

Answer

A/x-2 + B/(x+2)²

Answer

A/x+2 + B/(x-2)²

Answer

None of these

Answer 179

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

Answer 180

Ax+B/(x²+2)² + C/(x+1)²

Answer 181

A/(x²+2)² + B/(x+1)²

Answer 182

None of these

Answer 183

Linear equation

Answer 184

An equation

Answer 185

Cubic equation

Answer 186

An identity

Answer 187

A/x+1 + Bx+C/x²-x+1

Answer 188

A/x+1 – B/x²-x+1

Answer 189

Ax+B/x+1 + C/x²-x+1

Answer 190

A/x-1 – B/x²-x+1

Answer 191

Transcendental Equation

Answer 192

An equation

Answer 193

Cubic equation

Answer 194

Identity equation

Answer 195

Algebric equation

Answer 196

Algebric relation

Answer 197

None of these

Answer 198

Irreducible factor

Answer 199

Re placed factor

Answer 200

Reducible factor

Answer 201

Algebric equation

Answer 202

None of these

Answer 203

Improper fraction

Answer 204

Rational fraction

Answer 205

Proper fraction

Answer 206

None of these

Answer 207

Four kinds

Answer 208

Three kinds

Answer 209

(a + c)² = b² – c²

Answer 210

(a – c)² = b² + c²

Answer 211

(a – c)² = b² – c²

Answer 212

(a + c)² = b² + c²

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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Maan Ali

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