Mathematics Partial Fractions Online Test

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Question 1

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

Question 2

2. x + 3/x = 4 is

Answer

An identity

Answer

Cubic equation

Answer

A transcendental equation

Answer

An equation

Question 3

3. 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 4

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

Answer

Subtraction

Answer

Multiplication

Question 5

5. (x – 4)² = x² – 8x + 16 is

Answer

Cubic equation

Answer

An equation

Answer

Identity equation

Answer

Transcendental Equation

Question 6

6. 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 7

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

Answer

None of these

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

Question 8

8. 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 9

9. 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 10

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

Answer

An improper fraction

Answer

Algebraic equation

Answer

A proper fraction

Question 11

11. 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 12

12. x²–3/3x+1 is

Answer

None of these

Answer

Proper fraction

Answer

Rational fraction

Answer

Improper rational fraction

Question 13

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

Answer

2/3(x-2) – 4/3(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

Question 14

14. 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 15

15. 2x = 3 is a conditional equation it is true for

Question 16

16. 9x²/x³¯¹ is a fraction.

Answer

Rational fraction

Answer

None of these

Answer

Improper fraction

Answer

Proper fraction

Question 17

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

Answer

In equality

Answer

None of these

Question 18

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

Answer

Ax+B/x+1 + C/x²-x+1

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

Answer

P = 2, q = 1

Answer

P = 1, q = -1

Answer

P = -2, q = 1

Answer

P = 1, q = 1

Question 20

20. 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 + Bx+C/x²+1

Answer

A/x+1 + B/x²+1

Question 21

21. 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 22

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

Answer

Algebric equation

Answer

Algebric relation

Question 23

23. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

Answer

A = -1, B = 1

Answer

A = x-1, B = x + 1

Answer

A = 0, B = 2

Answer

A = x, B = 1

Question 24

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

Answer

Algebric equation

Answer

A proper fraction

Answer

Improper fraction

Question 25

25. 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 26

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

Answer

A/x+1 + Bx+C/x²-x+1

Answer

A/x-1 – B/x²-x+1

Answer

None of these

Answer

A/x+1 – B/x²-x+1

Question 27

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

Answer

Co-efficient

Question 28

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

Answer

Algebric equation

Answer

None of these

Question 29

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

Answer

A = 2, B = 3

Answer

A = 1, B = 3

Answer

A = 1, B = 5

Answer

A = 4, B = 3

Question 30

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

Answer

(Ax+B)(x²+x+1)+C(x²+x+1)²

Answer

A/x²+x+1 + B/(x²+x+1)²

Answer

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

Answer

None of these

Question 31

31. Which is a proper rational fraction?

Answer

None of these

Answer

2x²–5/x²+4

Answer

9x⁴/x³–1

Answer

2x–5/x²+4

Question 32

32. 1/(x+3)(x+2) =

Answer

1/x-3 – 1/x-2

Answer

1/x²-3 – 1/x²-2

Answer

None of these

Answer

1/x+3 – 1/x+2

Question 33

33. (x + 2)² = x² + 4x + 4 is

Answer

Cubic equation

Answer

An identity

Answer

An equation

Answer

Linear equation

Question 34

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

Answer

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

Answer

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

Answer

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

Answer

None of these

Question 35

35. 4x = 5 is ?

Answer

Conditional

Question 36

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

Answer

Combined fraction

Answer

Partial fraction

Answer

None of these

Answer

Rational fraction

Question 37

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

Question 38

38. 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 39

39. 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 40

40. The process of partial decomposition result in

Answer

Partial fraction

Answer

None of these

Answer

An identity

Question 41

41. (ax+b)/(cx +d)² =

Answer

None of these

Answer

A/cx+d + B/(cx+d)²

Answer

A/cx+d + B/cx+d

Answer

Ax+B/(cx+d)²

Question 42

42. 1/(x²+5)(x²+5) =

Answer

1/x²-4 – 1/x²+5

Answer

1/x²+4 – 1/x²+5

Answer

1/x²+4 – 1/x²-5

Answer

None of these

Question 43

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

Answer

None of these

Answer

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

Answer

Ax+B/(x²+2)² + C/(x+1)²

Answer

A/(x²+2)² + B/(x+1)²

Question 44

44. 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 + Bx+C/(x-1)² + D/(x-1)³

Answer

A/x-1 + B/(x-1)² + C/(x-1)³

Question 45

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

Question 46

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

Answer

Improper fraction

Answer

Combined fraction

Answer

None of these

Answer

Partial fraction

Question 47

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

Question 48

48. 1/(x – 3)(x – 2) =

Answer

1/x²-3 – 1/x-2

Answer

1/x-3 – 1/x-2

Answer

1/x+3 – 1/x+2

Answer

1/x²-3 – 1/x²-2

Question 49

49. There are _________ types of rational fraction.

Question 50

50. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

Answer

A = x, B = 1

Answer

A = 0, B = 2

Answer

A = x – 1, B = x + 1

Answer

A = -1, B = 1

Question 51

51. Rotational fraction are of

Answer

Three types

Answer

Four types

Question 52

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

Answer

Reducible factor

Answer

Irreducible factor

Answer

None of these

Answer

Re placed factor

Question 53

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

Question 54

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

Answer

A/x+1 + B/x-1

Answer

Ax+B/x²-1

Question 55

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

Answer

Algebric relation

Answer

A proper fraction

Answer

An improper fraction

Question 56

56. Algebric equation can be divided into

Answer

Four kinds

Answer

Three kinds

Question 57

57. x + 3/x = 4 is

Answer

An identity

Answer

An equation

Answer

A transcendental equation

Answer

Cubic equation

Question 58

58. 2x-5/x²+4 is ___________ rational fraction

Answer

None of these

Answer

Conditional

Question 59

59. (x+2)² = x² + 4x + 4 is

Answer

None of these

Answer

A linear equation

Answer

A quadratic equation

Answer

A cubic equation

Question 60

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

Answer

None of these

Answer

A/cx+d + bx/ex+f

Answer

A/cx+d + Bx/(ex+f)²

Answer

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

Question 61

61. 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 62

62. 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 63

63. P(x)/Q(x), Q(x) ≠ 0 is known as

Answer

None of these

Answer

Improper rational fraction

Answer

Proper rational fraction

Answer

Rational fraction

Question 64

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

Answer

Algebric relation

Answer

Algebric equation

Answer 178

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

Answer 179

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

Answer 180

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

Answer 181

3/x – 2/x+1

Answer 182

None of these

Answer 183

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

Answer 184

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

Answer 185

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

Answer 186

False Sentence

Answer 187

In Equation

Answer 188

True Sentence

Answer 189

None of these

Answer 190

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

Answer 191

A/x+1 + B/(x+1)² + C/x-1

Answer 192

A/x+1 + Bx+0/x²-1

Answer 193

1/a-b[1/x²+x+b – 1/x²+x+a]

Answer 194

1/a-b[1/x²+x+b +1/x²+x+a]

Answer 195

None of these

Answer 196

1/a-b[1/x²+x+a – 1/x²+x+b]

Answer 197

An equation

Answer 198

Cubic equation

Answer 199

A transcendental equation

Answer 200

An identity

Answer 201

A/x+2 + B/x-2

Answer 202

None of these

Answer 203

A/x-2 + B/(x+2)²

Answer 204

A/x+2 + B/(x-2)²

Answer 205

2/5(x+2) – 3/5(x+3)

Answer 206

2/5(x+2) + 3/5(x–3)

Answer 207

2/5(x–2) + 3/5(x+3)

Answer 208

2/5(x+2) – 3/5(x–3)

Answer 209

Two values of x

Answer 210

One value of x

Answer 211

None of these

Answer 212

All values of x

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?

Key Preparation Tips:

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