Mathematics Partial Fractions Online Test

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Question 1

1. 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 2

2. 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 3

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

Answer

A/(x²+2)² + B/(x+1)²

Answer

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

Answer

None of these

Answer

Ax+B/(x²+2)² + C/(x+1)²

Question 4

4. 2x = 3 is a conditional equation it is true for

Question 5

5. 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 = 2, q = 1

Answer

P = 1, q = 1

Answer

P = 1, q = -1

Question 6

6. 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 7

7. 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 8

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

Answer

True Sentence

Answer

False Sentence

Answer

In Equation

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. 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 11

11. 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 12

12. 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 13

13. 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 = x, B = 1

Answer

A = 0, B = 2

Question 14

14. 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 15

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

Answer

Co-efficient

Question 16

16. 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 + B/x²+1

Answer

A/x+1 + Bx+C/x²+1

Question 17

17. (x+2)² = x² + 4x + 4 is

Answer

A cubic equation

Answer

A quadratic equation

Answer

None of these

Answer

A linear equation

Question 18

18. 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 19

19. x + 3/x = 4 is

Answer

An equation

Answer

An identity

Answer

A transcendental equation

Answer

Cubic equation

Question 20

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

Answer

A/x+1 + B/x-1

Answer

Ax+B/x²-1

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

Question 23

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

Answer

Algebric relation

Answer

Algebric equation

Question 24

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

Answer

Combined fraction

Answer

Partial fraction

Answer

None of these

Answer

Rational fraction

Question 25

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

Question 26

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

Question 27

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

Question 28

28. The process of partial decomposition result in

Answer

None of these

Answer

Partial fraction

Answer

An identity

Question 29

29. (x – 4)² = x² + 8x + 16 is

Answer

A transcendental equation

Answer

An equation

Answer

Cubic equation

Answer

An identity

Question 30

30. 4x = 5 is ?

Answer

Conditional

Question 31

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

Answer

Improper fraction

Answer

Combined fraction

Answer

Partial fraction

Answer

None of these

Question 32

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

Answer

2/3(x-2) – 4/3(x+2)

Answer

3/x – 2/x+1

Answer

4/3(x-4) – 1/3(x-1)

Answer

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

Question 33

33. There are _________ types of rational fraction.

Question 34

34. 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 35

35. 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 36

36. (x + 2)² = x² + 4x + 4 is

Answer

Cubic equation

Answer

An equation

Answer

Linear equation

Answer

An identity

Question 37

37. 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 38

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

Question 39

39. Algebric equation can be divided into

Answer

Four kinds

Answer

Three kinds

Question 40

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

Answer

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

Answer

A/cx+d + bx/ex+f

Answer

A/cx+d + Bx/(ex+f)²

Answer

None of these

Question 41

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

Answer

A/x+1 + B/(x+1)² + C/x-1

Answer

None of these

Answer

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

Answer

A/x+1 + Bx+0/x²-1

Question 42

42. 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

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

Answer

None of these

Question 43

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

Question 44

44. x²–3/3x+1 is

Answer

Rational fraction

Answer

Proper fraction

Answer

Improper rational fraction

Answer

None of these

Question 45

45. 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 46

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

Answer

In equality

Answer

None of these

Question 47

47. 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 48

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

Answer

Irreducible factor

Answer

None of these

Answer

Reducible factor

Answer

Re placed factor

Question 49

49. 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

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

Ax+B/x-1 + C/(x-1)² + D/(x-1)³

Question 50

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

Answer

A/x-2 + B/(x+2)²

Answer

A/x+2 + B/x-2

Answer

None of these

Answer

A/x+2 + B/(x-2)²

Question 51

51. 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 52

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

Answer

Algebric equation

Answer

Algebric relation

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

Answer

None of these

Answer

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

Answer

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

Answer

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

Question 55

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

Answer

A = 1, B = 3

Answer

A = 4, B = 3

Answer

A = 2, B = 3

Answer

A = 1, B = 5

Question 56

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

Question 57

57. 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 58

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

Answer

Conditional

Answer

None of these

Question 59

59. x + 3/x = 4 is

Answer

An identity

Answer

A transcendental equation

Answer

An equation

Answer

Cubic equation

Question 60

60. 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 61

61. P(x)/Q(x), Q(x) ≠ 0 is known as

Answer

Improper rational fraction

Answer

Rational fraction

Answer

Proper rational fraction

Answer

None of these

Question 62

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

Answer

A proper fraction

Answer

An improper fraction

Answer

Algebraic equation

Question 63

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

Answer

None of these

Answer

A/x-1 – B/x²-x+1

Answer

A/x+1 + Bx+C/x²-x+1

Answer

A/x+1 – B/x²-x+1

Question 64

64. 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

None of these

Answer

1/a-b[1/x²+x+b – 1/x²+x+a]

Answer 175

Transcendental Equation

Answer 176

Identity equation

Answer 177

An equation

Answer 178

Cubic equation

Answer 179

Subtraction

Answer 180

Multiplication

Answer 181

1/x²-3 – 1/x²-2

Answer 182

1/x-3 – 1/x-2

Answer 183

1/x²-3 – 1/x-2

Answer 184

1/x+3 – 1/x+2

Answer 185

None of these

Answer 186

a² – c² = ab

Answer 187

a² + c² = – ab

Answer 188

a² – c² = – ab

Answer 189

Two values of x

Answer 190

All values of x

Answer 191

None of these

Answer 192

One value of x

Answer 193

Algebric equation

Answer 194

None of these

Answer 195

Improper fraction

Answer 196

Proper fraction

Answer 197

Rational fraction

Answer 198

None of these

Answer 199

Three types

Answer 200

Four types

Answer 201

1/x+3 – 1/x+2

Answer 202

1/x-3 – 1/x-2

Answer 203

None of these

Answer 204

1/x²-3 – 1/x²-2

Answer 205

Ax+B/x²+x+1 + Cx+D/(x²+x+1)

Answer 206

A/x²+x+1 + B/(x²+x+1)²

Answer 207

(Ax+B)(x²+x+1)+C(x²+x+1)²

Answer 208

None of these

Answer 209

None of these

Answer 210

A/cx+d + B/(cx+d)²

Answer 211

Ax+B/(cx+d)²

Answer 212

A/cx+d + B/cx+d

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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