Mathematics Partial Fractions Online Test

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Question 1

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

Answer

In Equation

Answer

False Sentence

Answer

True Sentence

Question 2

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

Answer

An improper fraction

Answer

A proper fraction

Answer

Algebraic equation

Question 3

3. Which is a proper rational fraction?

Answer

2x–5/x²+4

Answer

None of these

Answer

9x⁴/x³–1

Answer

2x²–5/x²+4

Question 4

4. 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 5

5. 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

None of these

Answer

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

Answer

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

Question 6

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

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

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

Question 7

7. Rotational fraction are of

Answer

Four types

Answer

Three types

Question 8

8. P(x)/Q(x), Q(x) ≠ 0 is known as

Answer

None of these

Answer

Rational fraction

Answer

Proper rational fraction

Answer

Improper rational fraction

Question 9

9. 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 10

10. x + 3/x = 4 is

Answer

An identity

Answer

An equation

Answer

A transcendental equation

Answer

Cubic equation

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. Algebric equation can be divided into

Answer

Three kinds

Answer

Four kinds

Question 13

13. 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 14

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

Answer

Co-efficient

Question 15

15. 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 16

16. 1/(x – 3)(x – 2) =

Answer

1/x²-3 – 1/x²-2

Answer

1/x+3 – 1/x+2

Answer

1/x²-3 – 1/x-2

Answer

1/x-3 – 1/x-2

Question 17

17. 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 18

18. (x+2)² = x² + 4x + 4 is

Answer

A quadratic equation

Answer

None of these

Answer

A linear equation

Answer

A cubic equation

Question 19

19. 9x²/x³¯¹ is a fraction.

Answer

Improper fraction

Answer

Rational fraction

Answer

Proper fraction

Answer

None of these

Question 20

20. 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 21

21. The process of partial decomposition result in

Answer

None of these

Answer

Partial fraction

Answer

An identity

Question 22

22. 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

A proper fraction

Answer

An improper fraction

Question 23

23. 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 24

24. 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 25

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

Answer

Algebric equation

Answer

Algebric relation

Question 26

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

Question 27

27. 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 28

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

Answer

Partial fraction

Answer

None of these

Answer

Improper fraction

Answer

Combined fraction

Question 29

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

Answer

A proper fraction

Answer

Algebric relation

Answer

An improper fraction

Question 30

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

Answer

In equality

Answer

None of these

Question 31

31. (x – 4)² = x² – 8x + 16 is

Answer

Identity equation

Answer

An equation

Answer

Transcendental Equation

Answer

Cubic equation

Question 32

32. 4x = 5 is ?

Answer

Conditional

Question 33

33. 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 34

34. There are _________ types of rational fraction.

Question 35

35. 2x-5/x²+4 is ___________ rational fraction

Answer

None of these

Answer

Conditional

Question 36

36. x + 3/x = 4 is

Answer

Cubic equation

Answer

A transcendental equation

Answer

An identity

Answer

An equation

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. 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 39

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

Question 40

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

Question 41

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

Answer

None of these

Answer

One value of x

Answer

All values of x

Answer

Two values of x

Question 42

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

Answer

None of these

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

Question 43

43. (x + 2)² = x² + 4x + 4 is

Answer

An equation

Answer

Linear equation

Answer

Cubic equation

Answer

An identity

Question 44

44. 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 45

45. 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 46

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

Answer

Ax+B/x²-1

Answer

A/x+1 + B/x-1

Question 47

47. 1/(x²+5)(x²+5) =

Answer

None of these

Answer

1/x²-4 – 1/x²+5

Answer

1/x²+4 – 1/x²-5

Answer

1/x²+4 – 1/x²+5

Question 48

48. 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 49

49. 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

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

Question 50

50. (x – 4)² = x² + 8x + 16 is

Answer

An equation

Answer

Cubic equation

Answer

An identity

Answer

A transcendental equation

Question 51

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

Answer

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

Answer

None of these

Answer

A/cx+d + Bx/(ex+f)²

Answer

A/cx+d + bx/ex+f

Question 52

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

Answer

Combined fraction

Answer

Rational fraction

Answer

None of these

Answer

Partial fraction

Question 53

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

Answer

4/3(x-4) – 1/3(x-1)

Answer

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

Answer

3/x – 2/x+1

Answer

2/3(x-2) – 4/3(x+2)

Question 54

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

Answer

None of these

Answer

Re placed factor

Answer

Reducible factor

Answer

Irreducible factor

Question 55

55. 1/(x+3)(x+2) =

Answer

1/x-3 – 1/x-2

Answer

1/x²-3 – 1/x²-2

Answer

1/x+3 – 1/x+2

Answer

None of these

Question 56

56. 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 57

57. 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 = -1, B = 1

Answer

A = 0, B = 2

Question 58

58. 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 59

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

Answer

Multiplication

Answer

Subtraction

Question 60

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

Question 61

61. 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 62

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

Answer

None of these

Answer

A/x+1 + Bx+C/x²+1

Answer

A/x+1 + B/x²+1

Answer

A/x-1 + B/x²+1

Question 63

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

Question 64

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

Answer 182

Algebric equation

Answer 183

Algebric relation

Answer 184

None of these

Answer 185

A/cx+d + B/cx+d

Answer 186

Ax+B/(cx+d)²

Answer 187

A/cx+d + B/(cx+d)²

Answer 188

A = 1, B = 3

Answer 189

A = 1, B = 5

Answer 190

A = 4, B = 3

Answer 191

A = 2, B = 3

Answer 192

Improper fraction

Answer 193

A proper fraction

Answer 194

Algebric equation

Answer 195

Algebric equation

Answer 196

None of these

Answer 197

None of these

Answer 198

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

Answer 199

A/(x²+2)² + B/(x+1)²

Answer 200

Ax+B/(x²+2)² + C/(x+1)²

Answer 201

Improper rational fraction

Answer 202

None of these

Answer 203

Proper fraction

Answer 204

Rational fraction

Answer 205

A/x+1 + Bx+C/x²-x+1

Answer 206

A/x+1 – B/x²-x+1

Answer 207

Ax+B/x+1 + C/x²-x+1

Answer 208

A/x-1 – B/x²-x+1

Answer 209

None of these

Answer 210

1/a-b[1/x²+x+a – 1/x²+x+b]

Answer 211

1/a-b[1/x²+x+b – 1/x²+x+a]

Answer 212

1/a-b[1/x²+x+b +1/x²+x+a]

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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