Mathematics Partial Fractions Online Test

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Question 1

1. 9x²/x³¯¹ is a fraction.

Answer

None of these

Answer

Proper fraction

Answer

Rational fraction

Answer

Improper fraction

Question 2

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

Answer

A/x+1 + Bx+C/x²+1

Answer

None of these

Answer

A/x-1 + B/x²+1

Answer

A/x+1 + B/x²+1

Question 3

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

Answer

(Ax+B)(x²+x+1)+C(x²+x+1)²

Answer

None of these

Answer

A/x²+x+1 + B/(x²+x+1)²

Answer

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

Question 4

4. Rotational fraction are of

Answer

Three types

Answer

Four types

Question 5

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

Answer

1/x²-3 – 1/x²-2

Answer

1/x-3 – 1/x-2

Answer

None of these

Answer

1/x+3 – 1/x+2

Question 6

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

Answer

In Equation

Answer

True Sentence

Answer

False Sentence

Question 7

7. Algebric equation can be divided into

Answer

Four kinds

Answer

Three kinds

Question 8

8. P(x)/Q(x), Q(x) ≠ 0 is known as

Answer

None of these

Answer

Rational fraction

Answer

Improper rational fraction

Answer

Proper rational fraction

Question 9

9. 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 10

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

Answer

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

Answer

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

Answer

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

Answer

None of these

Question 11

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

Answer

A/x+1 – B/x²-x+1

Answer

None of these

Answer

A/x-1 – B/x²-x+1

Answer

A/x+1 + Bx+C/x²-x+1

Question 12

12. x + 3/x = 4 is

Answer

An equation

Answer

Cubic equation

Answer

An identity

Answer

A transcendental equation

Question 13

13. The process of partial decomposition result in

Answer

None of these

Answer

An identity

Answer

Partial fraction

Question 14

14. (ax+b)/(cx +d)² =

Answer

None of these

Answer

A/cx+d + B/cx+d

Answer

Ax+B/(cx+d)²

Answer

A/cx+d + B/(cx+d)²

Question 15

15. 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 16

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

Answer

A/x+1 + B/(x+1)² + C/x-1

Answer

A/x+1 + Bx+0/x²-1

Answer

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

Answer

None of these

Question 17

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

Answer

3/x – 2/x+1

Answer

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

Answer

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

Answer

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

Question 18

18. There are _________ types of rational fraction.

Question 19

19. 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 20

20. (x+2)² = x² + 4x + 4 is

Answer

A cubic equation

Answer

None of these

Answer

A quadratic equation

Answer

A linear equation

Question 21

21. x-1/(x+2)(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)

Answer

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

Question 22

22. 4x = 5 is ?

Answer

Conditional

Question 23

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

Question 24

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

Answer

An improper fraction

Answer

Algebric relation

Answer

A proper fraction

Question 25

25. 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 26

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

Answer

Algebric equation

Answer

None of these

Question 27

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

Answer

None of these

Answer

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

Answer

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

Answer

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

Question 28

28. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

Answer

A = 0, B = 2

Answer

A = x, B = 1

Answer

A = x – 1, B = x + 1

Answer

A = -1, B = 1

Question 29

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

Answer

Algebraic equation

Answer

An improper fraction

Answer

A proper fraction

Question 30

30. 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

Reducible factor

Answer

Irreducible factor

Question 31

31. 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 32

32. Which is a proper rational fraction?

Answer

2x²–5/x²+4

Answer

2x–5/x²+4

Answer

None of these

Answer

9x⁴/x³–1

Question 33

33. (x – 4)² = x² + 8x + 16 is

Answer

A transcendental equation

Answer

An identity

Answer

An equation

Answer

Cubic equation

Question 34

34. 1/(x²+x+a)(x²+x+b) =

Answer

1/a-b[1/x²+x+b – 1/x²+x+a]

Answer

None of these

Answer

1/a-b[1/x²+x+a – 1/x²+x+b]

Answer

1/a-b[1/x²+x+b +1/x²+x+a]

Question 35

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

Answer

Algebraic equation

Answer

An improper fraction

Answer

A proper fraction

Question 36

36. 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 37

37. 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 38

38. 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

Ax+B/x+1 + C/x²-x+1

Answer

A/x+1 + Bx+C/x²-x+1

Question 39

39. (x + 2)² = x² + 4x + 4 is

Answer

Linear equation

Answer

An identity

Answer

Cubic equation

Answer

An equation

Question 40

40. 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 = 5

Answer

A = 1, B = 3

Answer

A = 2, B = 3

Question 41

41. 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 42

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

Answer

One value of x

Answer

All values of x

Answer

None of these

Answer

Two values of x

Question 43

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

Answer

None of these

Answer

A/x-2 + B/(x+2)²

Answer

A/x+2 + B/x-2

Answer

A/x+2 + B/(x-2)²

Question 44

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

Answer

Co-efficient

Question 45

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

Answer

Improper fraction

Answer

A proper fraction

Answer

Algebric equation

Question 46

46. 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 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. 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 49

49. x²–3/3x+1 is

Answer

Rational fraction

Answer

Proper fraction

Answer

Improper rational fraction

Answer

None of these

Question 50

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

Question 51

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

Answer

None of these

Answer

Rational fraction

Answer

Partial fraction

Answer

Combined fraction

Question 52

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

Answer

Algebric relation

Answer

Algebric equation

Question 53

53. 2x = 3 is a conditional equation it is true for

Question 54

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

Question 55

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

Question 56

56. x + 3/x = 4 is

Answer

Cubic equation

Answer

A transcendental equation

Answer

An equation

Answer

An identity

Question 57

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

Answer

Multiplication

Answer

Subtraction

Question 58

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

Answer

In equality

Answer

None of these

Question 59

59. 2x-5/x²+4 is ___________ rational fraction

Answer

None of these

Answer

Conditional

Question 60

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

Answer

A/cx+d + Bx/(ex+f)²

Answer

None of these

Answer

A/cx+d + bx/ex+f

Answer

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

Question 61

61. 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 62

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

Answer

Algebric relation

Answer

Algebric equation

Question 63

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

Question 64

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

Answer

A/x+1 + B/x-1

Answer

Ax+B/x²-1

Answer 184

A/(x²+2)² + B/(x+1)²

Answer 185

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

Answer 186

Ax+B/(x²+2)² + C/(x+1)²

Answer 187

None of these

Answer 188

1/x²+4 – 1/x²-5

Answer 189

1/x²+4 – 1/x²+5

Answer 190

None of these

Answer 191

1/x²-4 – 1/x²+5

Answer 192

2/x+1 – 7/(x+1)² + 9/(x-1)³

Answer 193

2/x+1 – 7/(x+1)² + 9/(x+1)³

Answer 194

2/x-1 – 7/(x-1)² + 9/(x-1)³

Answer 195

2/x-1 – 7/(x+1)² + 9/(x+1)³

Answer 196

Combined fraction

Answer 197

None of these

Answer 198

Partial fraction

Answer 199

Improper fraction

Answer 200

Cubic equation

Answer 201

Identity equation

Answer 202

An equation

Answer 203

Transcendental Equation

Answer 204

a² – c² = ab

Answer 205

a² – c² = – ab

Answer 206

a² + c² = – ab

Answer 207

None of these

Answer 208

A/x+1 + B/(x+1)² + C/(x+1)³

Answer 209

Ax+B/x-1 + C/(x-1)² + D/(x-1)³

Answer 210

A/x-1 + B/(x-1)² + C/(x-1)³

Answer 211

A/x-1 + Bx+C/(x-1)² + D/(x-1)³

Answer 212

(-π/2, π/2)

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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