Mathematics Partial Fractions Online Test

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Question 1

1. Which is a proper rational fraction?

Answer

9x⁴/x³–1

Answer

2x²–5/x²+4

Answer

None of these

Answer

2x–5/x²+4

Question 2

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

Answer

Reducible factor

Answer

Re placed factor

Answer

Irreducible factor

Answer

None of these

Question 3

3. x²–3/3x+1 is

Answer

Rational fraction

Answer

Improper rational fraction

Answer

None of these

Answer

Proper fraction

Question 4

4. x + 3/x = 4 is

Answer

An identity

Answer

A transcendental equation

Answer

Cubic equation

Answer

An equation

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. 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. There are _________ types of rational fraction.

Question 8

8. 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 9

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

Answer

Algebric equation

Answer

None of these

Question 10

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

Answer

A/x+1 – B/x²-x+1

Answer

A/x-1 – B/x²-x+1

Answer

None of these

Answer

A/x+1 + Bx+C/x²-x+1

Question 11

11. 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 12

12. 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 13

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

Answer

True Sentence

Answer

In Equation

Answer

False Sentence

Question 14

14. 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 15

15. 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 16

16. 1/(x²+5)(x²+5) =

Answer

1/x²+4 – 1/x²+5

Answer

1/x²-4 – 1/x²+5

Answer

None of these

Answer

1/x²+4 – 1/x²-5

Question 17

17. The process of partial decomposition result in

Answer

An identity

Answer

Partial fraction

Answer

None of these

Question 18

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

Question 19

19. (x+2)² = x² + 4x + 4 is

Answer

A linear equation

Answer

A quadratic equation

Answer

None of these

Answer

A cubic equation

Question 20

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

Answer

Partial fraction

Answer

Combined fraction

Answer

None of these

Answer

Improper fraction

Question 21

21. 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 22

22. 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 23

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

Answer

A/cx+d + Bx/(ex+f)²

Answer

None of these

Answer

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

Answer

A/cx+d + bx/ex+f

Question 24

24. 1/(x²+x+a)(x²+x+b) =

Answer

1/a-b[1/x²+x+a – 1/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

None of these

Question 25

25. (x – 4)² = x² – 8x + 16 is

Answer

Cubic equation

Answer

Transcendental Equation

Answer

An equation

Answer

Identity equation

Question 26

26. (x – 4)² = x² + 8x + 16 is

Answer

An identity

Answer

Cubic equation

Answer

An equation

Answer

A transcendental equation

Question 27

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

Answer

Algebric equation

Answer

Algebric relation

Question 28

28. 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 29

29. 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 30

30. Algebric equation can be divided into

Answer

Three kinds

Answer

Four kinds

Question 31

31. 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

A/(x²+2)² + B/(x+1)²

Answer

Ax+B/(x²+2)² + C/(x+1)²

Question 32

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

Answer

None of these

Answer

A/x+1 + B/x²+1

Answer

A/x+1 + Bx+C/x²+1

Answer

A/x-1 + B/x²+1

Question 33

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

Question 34

34. 2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

Answer

A = x – 1, B = x + 1

Answer

A = x, B = 1

Answer

A = 0, B = 2

Answer

A = -1, B = 1

Question 35

35. 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 + B/(x-1)² + C/(x-1)³

Answer

A/x-1 + Bx+C/(x-1)² + D/(x-1)³

Question 36

36. 2x-5/x²+4 is ___________ rational fraction

Answer

Conditional

Answer

None of these

Question 37

37. 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 38

38. 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 39

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

Answer

All values of x

Answer

None of these

Answer

One value of x

Answer

Two values of x

Question 40

40. (x + 2)² = x² + 4x + 4 is

Answer

An equation

Answer

Cubic equation

Answer

An identity

Answer

Linear equation

Question 41

41. 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 42

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

Question 43

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

Question 44

44. 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 45

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

Answer

Ax+B/x²-1

Answer

A/x+1 + B/x-1

Question 46

46. 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 47

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

Answer

None of these

Answer

In equality

Question 48

48. 2x = 3 is a conditional equation it is true for

Question 49

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

Answer

None of these

Answer

Partial fraction

Answer

Rational fraction

Answer

Combined fraction

Question 50

50. 9x²/x³¯¹ is a fraction.

Answer

Improper fraction

Answer

Rational fraction

Answer

None of these

Answer

Proper fraction

Question 51

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

Answer

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

Answer

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

Answer

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

Answer

None of these

Question 52

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

Question 53

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

Answer

A/x+1 + Bx+C/x²-x+1

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

Question 54

54. 4x = 5 is ?

Answer

Conditional

Question 55

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

Answer

Algebric equation

Answer

Algebric relation

Question 56

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

Question 57

57. 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 58

58. Rotational fraction are of

Answer

Three types

Answer

Four types

Question 59

59. 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 60

60. x + 3/x = 4 is

Answer

A transcendental equation

Answer

Cubic equation

Answer

An identity

Answer

An equation

Question 61

61. P(x)/Q(x), Q(x) ≠ 0 is known as

Answer

Rational fraction

Answer

Proper rational fraction

Answer

Improper rational fraction

Answer

None of these

Question 62

62. 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 63

63. 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 64

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

Answer

Subtraction

Answer

Multiplication

Answer 177

(Ax+B)(x²+x+1)+C(x²+x+1)²

Answer 178

A/x²+x+1 + B/(x²+x+1)²

Answer 179

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

Answer 180

None of these

Answer 181

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

Answer 182

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

Answer 183

3/x – 2/x+1

Answer 184

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

Answer 185

A = x-1, B = x + 1

Answer 186

A = -1, B = 1

Answer 187

A = 0, B = 2

Answer 188

A = x, B = 1

Answer 189

A = 4, B = 3

Answer 190

A = 1, B = 3

Answer 191

A = 1, B = 5

Answer 192

A = 2, B = 3

Answer 193

None of these

Answer 194

A/cx+d + B/(cx+d)²

Answer 195

Ax+B/(cx+d)²

Answer 196

A/cx+d + B/cx+d

Answer 197

1/x²-3 – 1/x²-2

Answer 198

1/x+3 – 1/x+2

Answer 199

1/x²-3 – 1/x-2

Answer 200

1/x-3 – 1/x-2

Answer 201

None of these

Answer 202

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

Answer 203

A/x+1 + B/(x+1)² + C/x-1

Answer 204

A/x+1 + Bx+0/x²-1

Answer 205

Co-efficient

Answer 206

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

Answer 207

None of these

Answer 208

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

Answer 209

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

Answer 210

Algebraic equation

Answer 211

A proper fraction

Answer 212

An improper fraction

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

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