Simplification


  1. If   I =
    3
    ÷
    5
    , II = 3 ÷ [(4 ÷ 5) ÷ 6],
    46

    III = [3 ÷ (4 ÷ 5)] ÷ 6, IV = 3 ÷ 4 (5 ÷ 6) then









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    I. =
    3
    ×
    6
    =
    9
    4510

    II. = 3 ÷
    4
    ×
    1
    = 3 ÷
    2
    =
    45
    56152

    III. = 3 ÷
    4
    ÷ 6 =
    15
    ÷ 6 =
    5
    548

    IV. = 3 ÷ 4 ×
    5
    = 3 ÷
    10
    =
    9
    6310

    Obviously, (I) and (IV) are equal

    Correct Option: B

    I. =
    3
    ×
    6
    =
    9
    4510

    II. = 3 ÷
    4
    ×
    1
    = 3 ÷
    2
    =
    45
    56152

    III. = 3 ÷
    4
    ÷ 6 =
    15
    ÷ 6 =
    5
    548

    IV. = 3 ÷ 4 ×
    5
    = 3 ÷
    10
    =
    9
    6310

    Obviously, (I) and (IV) are equal


  1. 1
    +
    1
    +
    1
    +
    1
    +
    1
    +
    1
    = ?
    3042567290110









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    1
    +
    1
    +
    1
    +
    1
    +
    1
    +
    1
    5 × 66 × 77 × 88 × 99 × 1010 × 11

    =
    1
    1
    +
    1
    1
    +
    1
    1
    +
    1
    1
    +
    1
    1
    +
    1
    1
    566778899101011

    =
    1
    1
    =
    11 − 5
    =
    6
    5115555

    Correct Option: D

    1
    +
    1
    +
    1
    +
    1
    +
    1
    +
    1
    5 × 66 × 77 × 88 × 99 × 1010 × 11

    =
    1
    1
    +
    1
    1
    +
    1
    1
    +
    1
    1
    +
    1
    1
    +
    1
    1
    566778899101011

    =
    1
    1
    =
    11 − 5
    =
    6
    5115555



  1. The value of
    0.1 × 0.1 × 0.1 + 0.2 ×0.2 × 0.2 + 0.3 × 0.3 × 0.3 − 3 × 0.1 × 0.2 × 0.3
    0.1 × 0.1 + 0.2 × 0.2 + 0.3 × 0.3 − 0.1 × 0.2 − 0.2 × 0.3 − 0.3 × 0.1
    is









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    Using (x) of Basic Formulae
    Let 0.1 = a, 0.2 = b and 0.3 = c
    Then, we have,

    a × a × a + b × b × b + c × c × c − 3abc
    a × a + b × b + c × c − ab − bc − ac

    =
    a3 + b3 + c3 − 3abc
    a2 + b2 + c2 − ab − bc − ac

    = a + b + c
    = 0.1 + 0.2 + 0.3 = 0.6

    Correct Option: B

    Using (x) of Basic Formulae
    Let 0.1 = a, 0.2 = b and 0.3 = c
    Then, we have,

    a × a × a + b × b × b + c × c × c − 3abc
    a × a + b × b + c × c − ab − bc − ac

    =
    a3 + b3 + c3 − 3abc
    a2 + b2 + c2 − ab − bc − ac

    = a + b + c
    = 0.1 + 0.2 + 0.3 = 0.6


  1. Simplify









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    =
    13
    ÷
    1
    =
    13
    4246

    =
    13
    × 24 =
    13
    46

    = 13 × 6 ×
    6
    = 36
    13

    Correct Option: B


    =
    13
    ÷
    1
    =
    13
    4246

    =
    13
    × 24 =
    13
    46

    = 13 × 6 ×
    6
    = 36
    13




  1. is equal to









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    =
    31
    ×
    30
    5
    1252

    =
    31
    5
    =
    31 − 5
    =
    26
    2222

    = 13

    Correct Option: C


    =
    31
    ×
    30
    5
    1252

    =
    31
    5
    =
    31 − 5
    =
    26
    2222

    = 13