-- advertisement --

Order of Magnitude

  1. If x = √3 + √2, then the value of (x + 1)/(x - 1) - (x - 1)/(x + 1) is ?
    1. √3
    2. √2
    3. √6
    4. None of above
  1. View Hint | View Answer | Workspace | Discuss In Forum | Report

    (x + 1)/(x - 1) - (x - 1)/(x + 1) = {(x + 1)2 - (x - 1)2} / {(x - 1) (x + 1)}
    = (x2 + 1 + 2x) - (x2 + 1 - 2x) / (x2 - 1)
    = 4x / (x2 - 1) = 4(√3 + √2) / {(√3 + √2)2 - 1}

    Correct Option: B

    (x + 1)/(x - 1) - (x - 1)/(x + 1) = {(x + 1)2 - (x - 1)2} / {(x - 1) (x + 1)}
    = (x2 + 1 + 2x) - (x2 + 1 - 2x) / (x2 - 1)
    = 4x / (x2 - 1) = 4(√3 + √2) / {(√3 + √2)2 - 1}
    = 4(√3 + √2) / (3 + 2 + 2√6 - 1) = 4(√3 + √2) / (4 + 2 √6)
    = 4(√3 + √2) / 2 √2 (√3 + √2)
    = √2

    Report

  1. Which among ∛8 and ∛1000 is greater ?
    1. ∛8
    2. ∛1000
    3. Both are equal
    4. None of these
  1. View Hint | View Answer | Workspace | Discuss In Forum | Report

    ∛8 and ∛1000 = 81/3 and 10001/3

    Correct Option: B

    ∛8 and ∛1000 = 81/3 and 10001/3
    Since 1000 > 8
    ∴ ∛1000 > ∛8

    Report

-- advertisement --


  1. Which among √81 and √1 is smaller ?
    1. √81
    2. √1
    3. Both are equal
    4. None of these
  1. View Hint | View Answer | Workspace | Discuss In Forum | Report

    √81 and √1 = 811/2 and 11/2

    Correct Option: B

    √81 and √1 = 811/2 and 11/2
    Since, 1 < 81
    ∴ √1 < √81

    Report

  1. IF (14)3 is added to the square of a number, the answer to obtained is 4425. What is the number ?
    1. 1849
    2. 43
    3. 41
    4. 1681
  1. View Hint | View Answer | Workspace | Discuss In Forum | Report

    Let the number be x.
    According to the question,
    x2 + (14)3 = 4425

    Correct Option: C

    Let the number be x.
    According to the question,
    x2 + (14)3 = 4425
    ⇒ x2 = 4425 - (14)3
    ⇒ x2 = 4425 - 2744
    ⇒ x2 = 1681
    ∴ x = √1681 = 41

    Report

  1. Which among ∜10 and ∛8 is greater ?
    1. ∛10
    2. ∛8
    3. Both are equal
    4. None of these
  1. View Hint | View Answer | Workspace | Discuss In Forum | Report

    ∜10 and ∛8 = 101/4 and 81/3
    Since, LCM of 4 and 3 is 12.
    ∴ 101/4 = 103/12 = (103)1/12 = (1000)1/12 = 121000
    and 81/3 = 84/12 = (84)1/12 (4096)1/2 = 124096
    ∴ 4096 > 1000

    Correct Option: B

    ∜10 and ∛8 = 101/4 and 81/3
    Since, LCM of 4 and 3 is 12.
    ∴ 101/4 = 103/12 = (103)1/12 = (1000)1/12 = 121000
    and 81/3 = 84/12 = (84)1/12 (4096)1/2 = 124096
    ∴ 4096 > 1000
    Hence, 81/3 >101/4
    ∴ ∛8 > ∜10

    Report

-- advertisement --

-- advertisement --