Algebra


  1. If   x =
    5 + 1
    then the value of 5x2 – 5x – 1 is
    5 − 1









  1. View Hint View Answer Discuss in Forum


    = 5
    (√5 + 1)
    2 − 5
    (√5 + 1)
    − 1
    22

    = 5
    5 + 1 + 2√5
    5√5 + 5
    − 1
    42

    = 5
    3 + √5
    5√5 + 5
    − 1
    22

    =
    15 + 5√5 − 5√5 − 5 − 2
    2

    =
    8
    = 4
    2

    Correct Option: C


    = 5
    (√5 + 1)
    2 − 5
    (√5 + 1)
    − 1
    22

    = 5
    5 + 1 + 2√5
    5√5 + 5
    − 1
    42

    = 5
    3 + √5
    5√5 + 5
    − 1
    22

    =
    15 + 5√5 − 5√5 − 5 − 2
    2

    =
    8
    = 4
    2


  1. If  
    2a + b
    = 3, then find the value of
    a + b
    a + 4ba + 2b









  1. View Hint View Answer Discuss in Forum

    2a + b
    = 3 (Given)
    a + 4b

    ⇒  2a + b = 3a + 12b
    ⇒  3a – 2a = b – 12 b
    ⇒  a = – 11b
    Then,  
    a + b
    =
    − 11b + b
    a + 2b− 11b + 2b

    =
    −10b
    =
    10
    −9b9

    Correct Option: C

    2a + b
    = 3 (Given)
    a + 4b

    ⇒  2a + b = 3a + 12b
    ⇒  3a – 2a = b – 12 b
    ⇒  a = – 11b
    Then,  
    a + b
    =
    − 11b + b
    a + 2b− 11b + 2b

    =
    −10b
    =
    10
    −9b9



  1. If a * b = 2 (a + b), then 5 * 2 is equal to :









  1. View Hint View Answer Discuss in Forum

    a * b = 2 (a + b)
    ∴  5 * 2 = 2 (5 + 2)
    = 2 × 7 = 14

    Correct Option: C

    a * b = 2 (a + b)
    ∴  5 * 2 = 2 (5 + 2)
    = 2 × 7 = 14


  1. 1 +
    1
    x + 4









  1. View Hint View Answer Discuss in Forum

    Given expression

    = 1 +
    1
    1 +
    1
    1 +
    1
    1 +
    1
    xx + 1x + 2x + 3

    =
    x + 1
    ×
    x + 2
    ×
    x + 3
    ×
    x + 4
    xx + 1x + 2x + 3

    =
    x + 4
    x

    Correct Option: D

    Given expression

    = 1 +
    1
    1 +
    1
    1 +
    1
    1 +
    1
    xx + 1x + 2x + 3

    =
    x + 1
    ×
    x + 2
    ×
    x + 3
    ×
    x + 4
    xx + 1x + 2x + 3

    =
    x + 4
    x



  1. Two numbers x and y (x > y) are such that their sum is equal to three times their difference.
    Then value of  
    3xy
      will be:
    2(x2 − y2)









  1. View Hint View Answer Discuss in Forum

    (x + y) = 3 (x – y) = 3x – 3y
    ⇒  3y + y = 3x – x
    ⇒  2x = 4y
    ⇒  x = 2y

    ⇒ 
    x
    =
    2
    y1

    ∴  x = 2, y = 1
    3xy
    =
    3 × 2 × 1
    =
    6
    = 1
    2(x2 − y2)2 × (4 − 1)6

    Correct Option: B

    (x + y) = 3 (x – y) = 3x – 3y
    ⇒  3y + y = 3x – x
    ⇒  2x = 4y
    ⇒  x = 2y

    ⇒ 
    x
    =
    2
    y1

    ∴  x = 2, y = 1
    3xy
    =
    3 × 2 × 1
    =
    6
    = 1
    2(x2 − y2)2 × (4 − 1)6