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Aptitude miscellaneous
  1. The value of ( x + y + z )³ – ( y + z - x )³ – ( z + x - y )³ – ( x + y - z )³ is :








  1. View Hint View Answer Discuss in Forum

    If x = y = z = 1, then
    Expression = (3)3 – (1)3 – (1)3 – (1)3
    = 27 – 3 = 24 = 24xyz

    Correct Option: B

    If x = y = z = 1, then
    Expression = (3)3 – (1)3 – (1)3 – (1)3
    = 27 – 3 = 24 = 24xyz

  1. If a + b + c = 0, then a3 + b3 + c3 is equal to








  1. View Hint View Answer Discuss in Forum

    Using Rule 21,
    ∴ a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
    If a + b + c = 0, then a3 + b3 + c3 = 3abc

    Correct Option: D

    Using Rule 21,
    ∴ a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
    If a + b + c = 0, then a3 + b3 + c3 = 3abc

  1. If x = a – b, y = b – c, z = c – a, then the numerical value of the algebraic expression x3 + y3 + z3 – 3xyz will be








  1. View Hint View Answer Discuss in Forum

    x + y + z = a – b + b – c + c – a = 0
    ∴ x3 + y3 + z3 – 3xyz = 0

    Correct Option: B

    x + y + z = a – b + b – c + c – a = 0
    ∴ x3 + y3 + z3 – 3xyz = 0

  1. If x =
    √3 - √2
    		and y =
    √3 + √2
    		, then the value of x3 + y3 is :
    √3 + √2√3 - √2









  1. View Hint View Answer Discuss in Forum

    x =
    ( √3 - √2 )
    ( √3 + √2 )

    ⇒ x =
    ( √3 - √2 ) ( √3 - √2 )
    ( √3 + √2 )( √3 - √2 )

    ⇒ x =
    ( √3 - √2 )2
    3 - 2

    = 3 + 2 – 2.√3.√2
    = 5 - 2√6
    ∴ y =
    ( √3 + √2 )
    		 = 5 + 2√6
    ( √3 - √2 )

    ∴ x + y = 5 - 2√6 + 5 + 2√6 = 10
    xy = ( 5 - 2√6 )( 5 + 2√6 )
    = 25 – 24 = 1
    ∴ x3 + y3 = ( x + y )3 - 3xy( x + y )
    = (10)3 – 3(10)
    = 1000 – 30 = 970

    Correct Option: D

    x =
    ( √3 - √2 )
    ( √3 + √2 )

    ⇒ x =
    ( √3 - √2 ) ( √3 - √2 )
    ( √3 + √2 )( √3 - √2 )

    ⇒ x =
    ( √3 - √2 )2
    3 - 2

    = 3 + 2 – 2.√3.√2
    = 5 - 2√6
    ∴ y =
    ( √3 + √2 )
    		 = 5 + 2√6
    ( √3 - √2 )

    ∴ x + y = 5 - 2√6 + 5 + 2√6 = 10
    xy = ( 5 - 2√6 )( 5 + 2√6 )
    = 25 – 24 = 1
    ∴ x3 + y3 = ( x + y )3 - 3xy( x + y )
    = (10)3 – 3(10)
    = 1000 – 30 = 970

  1. If (x – a) (x – b) = 1 and a – b + 5= 0, then the value of ( x - a )3 -
    1
    		 is :
    ( x - a )3









  1. View Hint View Answer Discuss in Forum

    (x - a)3 -
    1
    		 = (x - a) -
    1
    		3 - 3(x - a) -
    1
    (x - a)3(x - a)(x - a)

    = (x – a – x + b)3 + 3(x – a – x + b)
    = (b - a)3 + 3(b – a)
    = 53 + 3 × 5 = 125 + 15 = 140

    Correct Option: D

    (x - a)3 -
    1
    		 = (x - a) -
    1
    		3 - 3(x - a) -
    1
    (x - a)3(x - a)(x - a)

    = (x – a – x + b)3 + 3(x – a – x + b)
    = (b - a)3 + 3(b – a)
    = 53 + 3 × 5 = 125 + 15 = 140