Mathematics Partial Fractions Online Test

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Question 1

1. 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 + B/1-bx + C/1-cx

Answer

None of these

Answer

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

Question 2

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

Answer

None of these

Answer

A/x+2 + B/x-2

Answer

A/x+2 + B/(x-2)²

Answer

A/x-2 + B/(x+2)²

Question 3

3. 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 4

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

Answer

Co-efficient

Question 5

5. (ax+b)/(cx +d)² =

Answer

Ax+B/(cx+d)²

Answer

A/cx+d + B/(cx+d)²

Answer

A/cx+d + B/cx+d

Answer

None of these

Question 6

6. 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 7

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

Question 8

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

Question 9

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

Answer

None of these

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

Question 10

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

Answer

One value of x

Answer

None of these

Answer

Two values of x

Answer

All values of x

Question 11

11. 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 = 1, q = -1

Answer

P = -2, q = 1

Question 12

12. 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 13

13. 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 14

14. x + 3/x = 4 is

Answer

A transcendental equation

Answer

Cubic equation

Answer

An equation

Answer

An identity

Question 15

15. 1/(x+3)(x+2) =

Answer

1/x+3 – 1/x+2

Answer

1/x-3 – 1/x-2

Answer

None of these

Answer

1/x²-3 – 1/x²-2

Question 16

16. x²–3/3x+1 is

Answer

None of these

Answer

Proper fraction

Answer

Improper rational fraction

Answer

Rational fraction

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

Answer

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

Question 18

18. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

Answer

A = x, B = 1

Answer

A = x-1, B = x + 1

Answer

A = 0, B = 2

Answer

A = -1, B = 1

Question 19

19. There are _________ types of rational fraction.

Question 20

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

Question 21

21. 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 22

22. Algebric equation can be divided into

Answer

Four kinds

Answer

Three kinds

Question 23

23. The process of partial decomposition result in

Answer

An identity

Answer

Partial fraction

Answer

None of these

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. 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 26

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

Answer

Algebric relation

Answer

Algebric equation

Question 27

27. (x + 2)² = x² + 4x + 4 is

Answer

Linear equation

Answer

Cubic equation

Answer

An identity

Answer

An equation

Question 28

28. 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 29

29. x + 3/x = 4 is

Answer

An identity

Answer

Cubic equation

Answer

A transcendental equation

Answer

An equation

Question 30

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

Answer

A/x²+x+1 + B/(x²+x+1)²

Answer

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

Answer

(Ax+B)(x²+x+1)+C(x²+x+1)²

Answer

None of these

Question 31

31. 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 32

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

Question 33

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

Answer

Re placed factor

Answer

Irreducible factor

Answer

None of these

Answer

Reducible factor

Question 34

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

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 + Bx+C/(x-1)² + D/(x-1)³

Answer

A/x+1 + B/(x+1)² + C/(x+1)³

Question 35

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

Question 36

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

Answer

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

Answer

4/3(x-4) – 1/3(x-1)

Answer

3/x – 2/x+1

Answer

2/3(x-2) – 4/3(x+2)

Question 37

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

Answer

Ax+B/x²-1

Answer

A/x+1 + B/x-1

Question 38

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

Question 39

39. 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 40

40. 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 41

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

Answer

Algebric equation

Answer

None of these

Question 42

42. (x+2)² = x² + 4x + 4 is

Answer

None of these

Answer

A cubic equation

Answer

A quadratic equation

Answer

A linear equation

Question 43

43. 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 44

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

Answer

Algebric relation

Answer

An improper fraction

Answer

A proper fraction

Question 45

45. 1/(x – 3)(x – 2) =

Answer

1/x-3 – 1/x-2

Answer

1/x+3 – 1/x+2

Answer

1/x²-3 – 1/x-2

Answer

1/x²-3 – 1/x²-2

Question 46

46. Rotational fraction are of

Answer

Three types

Answer

Four types

Question 47

47. 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 48

48. 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 49

49. 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 50

50. (x – 4)² = x² – 8x + 16 is

Answer

An equation

Answer

Transcendental Equation

Answer

Identity equation

Answer

Cubic equation

Question 51

51. 2x-5/x²+4 is ___________ rational fraction

Answer

None of these

Answer

Conditional

Question 52

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

Answer

Partial fraction

Answer

None of these

Answer

Combined fraction

Answer

Improper fraction

Question 53

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

Answer

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

Answer

None of these

Answer

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

Answer

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

Question 54

54. P(x)/Q(x), Q(x) ≠ 0 is known as

Answer

None of these

Answer

Improper rational fraction

Answer

Rational fraction

Answer

Proper rational fraction

Question 55

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

Answer

In Equation

Answer

True Sentence

Answer

False Sentence

Question 56

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

Answer

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

Answer

A/cx+d + bx/ex+f

Answer

None of these

Answer

A/cx+d + Bx/(ex+f)²

Question 57

57. (x – 4)² = x² + 8x + 16 is

Answer

A transcendental equation

Answer

An identity

Answer

An equation

Answer

Cubic equation

Question 58

58. 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 = 2, B = 3

Answer

A = 1, B = 5

Answer

A = 1, B = 3

Question 59

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

Answer

Algebric relation

Answer

Algebric equation

Question 60

60. 4x = 5 is ?

Answer

Conditional

Question 61

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

Question 62

62. 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 + Bx+C/x²-x+1

Answer

A/x-1 – B/x²-x+1

Question 63

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

Answer

A/x+1 + B/x²+1

Answer

A/x+1 + Bx+C/x²+1

Answer

None of these

Answer

A/x-1 + B/x²+1

Question 64

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

Answer

Multiplication

Answer

Subtraction

Answer 183

A proper fraction

Answer 184

Algebric equation

Answer 185

Improper fraction

Answer 186

Improper fraction

Answer 187

Proper fraction

Answer 188

Rational fraction

Answer 189

None of these

Answer 190

Ax+B/x+1 + C/x²-x+1

Answer 191

A/x+1 – B/x²-x+1

Answer 192

A/x-1 – B/x²-x+1

Answer 193

A/x+1 + Bx+C/x²-x+1

Answer 194

(-π/2, π/2)

Answer 195

None of these

Answer 196

Partial fraction

Answer 197

Combined fraction

Answer 198

Rational fraction

Answer 199

2x²–5/x²+4

Answer 200

2x–5/x²+4

Answer 201

9x⁴/x³–1

Answer 202

None of these

Answer 203

2/x+1 – 7/(x+1)² + 9/(x+1)³

Answer 204

2/x-1 – 7/(x+1)² + 9/(x+1)³

Answer 205

2/x-1 – 7/(x-1)² + 9/(x-1)³

Answer 206

2/x+1 – 7/(x+1)² + 9/(x-1)³

Answer 207

None of these

Answer 208

In equality

Answer 209

A/(x²+2)² + B/(x+1)²

Answer 210

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

Answer 211

Ax+B/(x²+2)² + C/(x+1)²

Answer 212

None of these

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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