Simplification

Simplification

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Aptitude miscellaneous
  1. (5.5)3 – (4.5)3 is equal to :








  1. View Hint View Answer Discuss in Forum

    (5.5)3 – (4.5)3
    = (5.5 – 4.5)3 + 3 × 5.5 × 4.5 (5.5 – 4.5)
    = (1)3 + 74.25 (1)
    = 1 + 74.25 = 75.25

    Correct Option: D

    (5.5)3 – (4.5)3
    = (5.5 – 4.5)3 + 3 × 5.5 × 4.5 (5.5 – 4.5)
    = (1)3 + 74.25 (1)
    = 1 + 74.25 = 75.25

  1. 3√
    72.9
    		   is equal to :
    0.4096








  1. View Hint View Answer Discuss in Forum

    3√
    72.9
    		 = 3√
    729000
    0.40964096

    3√
    (90)3
    		 =
    90
    (16)316

    =
    45
    		 = 5.625
    8

    Correct Option: B

    3√
    72.9
    		 = 3√
    729000
    0.40964096

    3√
    (90)3
    		 =
    90
    (16)316

    =
    45
    		 = 5.625
    8

  1. 3√8
    		÷ √
    100
    		×3√125   is equal to :
    √1649








  1. View Hint View Answer Discuss in Forum

    On simplification,

    Expression =
    2
    		 ×
    7
    		 × 5
    410

    =
    7
    		 = 1
    3
    44

    Correct Option: B

    On simplification,

    Expression =
    2
    		 ×
    7
    		 × 5
    410

    =
    7
    		 = 1
    3
    44

  1. The sum of the cubes of the numbers 22, –15 and –7 is equal to








  1. View Hint View Answer Discuss in Forum

    Here, 22 – 15 – 7 = 0
    We know that
    a3 + b3 + c3 = 3abc,
    if a + b + c = 0
    ∴  (22)3 + (–15)3 + (–7)3
    = 3 × 22 × (–15) (–7) = 6930

    Correct Option: A

    Here, 22 – 15 – 7 = 0
    We know that
    a3 + b3 + c3 = 3abc,
    if a + b + c = 0
    ∴  (22)3 + (–15)3 + (–7)3
    = 3 × 22 × (–15) (–7) = 6930

  1. The least number to be subtracted from 16800 to make it a perfect square is








  1. View Hint View Answer Discuss in Forum


    ∴  Required number = 159
    16800 – 159 = 16641
    and √16641 = 129

    Correct Option: C


    ∴  Required number = 159
    16800 – 159 = 16641
    and √16641 = 129