Algebra


  1. What should be added to 8 (3x – 4y) to obtain (18x – 18y) ?









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    Required answer
    = (18x – 18y) – 8 (3x – 4y)
    = 18x – 18y – 24x + 32y
    = 14y – 6x

    Correct Option: C

    Required answer
    = (18x – 18y) – 8 (3x – 4y)
    = 18x – 18y – 24x + 32y
    = 14y – 6x


  1. x2 + 3x + 1
    =
    1
    , then the value of x +
    1
    is :
    x2 − 3x + 12x









  1. View Hint View Answer Discuss in Forum

    x2 + 3x + 1
    =
    1
    x2 − 3x + 12

    ⇒  2x2 + 6x + 2 = x2 – 3x + 1
    ⇒  2x2 – x2 + 2 – 1 = – 6x – 3x
    ⇒  x2 + 1 = – 9x
    ⇒ 
    x2 + 1
    = –9
    x

    ⇒  x +
    1
    = –9
    x

    Correct Option: B

    x2 + 3x + 1
    =
    1
    x2 − 3x + 12

    ⇒  2x2 + 6x + 2 = x2 – 3x + 1
    ⇒  2x2 – x2 + 2 – 1 = – 6x – 3x
    ⇒  x2 + 1 = – 9x
    ⇒ 
    x2 + 1
    = –9
    x

    ⇒  x +
    1
    = –9
    x



  1. If (a + b)2 = 100 and (a – b) = 4, then ab equals to :









  1. View Hint View Answer Discuss in Forum

    4ab = (a + b)2 – (a – b)2
    ⇒  4ab = 100 – (4)2 = 100 – 16
    ⇒  4ab = 84

    ⇒  ab =
    84
    = 21
    4

    Correct Option: C

    4ab = (a + b)2 – (a – b)2
    ⇒  4ab = 100 – (4)2 = 100 – 16
    ⇒  4ab = 84

    ⇒  ab =
    84
    = 21
    4


  1. If   4x +
    1
    = 5, x ≠ 0, then the value of
    5x
    is :
    x4x2 + 10x + 1









  1. View Hint View Answer Discuss in Forum

    4x +
    1
    = 5
    x

    Expression =
    5x
    4x2 + 1 + 10x

    =
    5x
    x4x +
    1
    + 10
    x

    =
    5
    =
    5
    =
    1
    5 + 10153

    Correct Option: B

    4x +
    1
    = 5
    x

    Expression =
    5x
    4x2 + 1 + 10x

    =
    5x
    x4x +
    1
    + 10
    x

    =
    5
    =
    5
    =
    1
    5 + 10153



  1. If  
    a
    +
    b
    +
    c
    =
    1
    , then the value of
    1 − 2a1 − 2b1 − 2c2
    1
    +
    1
    +
    1
    is :
    1 − 2a1 − 2b1 − 2c









  1. View Hint View Answer Discuss in Forum

    a
    +
    b
    +
    c
    =
    1
    1 − 2a1 − 2b1 − 2c2

    ⇒ 
    2a
    +
    2b
    +
    2c
    =
    2
    = 1
    1 − 2a1 − 2b1 − 2c2

    ⇒ 
    2a
    + 1 +
    2b
    + 1 +
    2c
    + 1 = 4
    1 − 2a1 − 2b1 − 2c

    ⇒ 
    2a + 1 − 2a
    +
    2b + 1 − 2b
    +
    2c + 1 − 2c
    = 4
    1 − 2a1 − 2b1 − 2c

    ⇒ 
    1
    +
    1
    +
    1
    = 4
    1 − 2a1 − 2b1 − 2c

    Correct Option: D

    a
    +
    b
    +
    c
    =
    1
    1 − 2a1 − 2b1 − 2c2

    ⇒ 
    2a
    +
    2b
    +
    2c
    =
    2
    = 1
    1 − 2a1 − 2b1 − 2c2

    ⇒ 
    2a
    + 1 +
    2b
    + 1 +
    2c
    + 1 = 4
    1 − 2a1 − 2b1 − 2c

    ⇒ 
    2a + 1 − 2a
    +
    2b + 1 − 2b
    +
    2c + 1 − 2c
    = 4
    1 − 2a1 − 2b1 − 2c

    ⇒ 
    1
    +
    1
    +
    1
    = 4
    1 − 2a1 − 2b1 − 2c