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Aptitude miscellaneous
  1. If   x3 −
    2
    		 =
    3
    		 = , then the value of   x2 +
    1
    		   is
    xxx2








  1. View Hint View Answer Discuss in Forum

    3x − 2 =
    3
    x

    ⇒  3x −
    3
    		 = 2
    x

    ⇒  x −
    1
    		 =
    2
    x3

    On squaring both sides
    x −
    1
    		2 =
    4
    x9

    ⇒  x2 +
    1
    		 − 2 =
    4
    x29

    ⇒  x2 +
    1
    x2

    =
    4
    		 + 2 =
    22
    		 = 2
    4
    999

    Correct Option: B

    3x − 2 =
    3
    x

    ⇒  3x −
    3
    		 = 2
    x

    ⇒  x −
    1
    		 =
    2
    x3

    On squaring both sides
    x −
    1
    		2 =
    4
    x9

    ⇒  x2 +
    1
    		 − 2 =
    4
    x29

    ⇒  x2 +
    1
    x2

    =
    4
    		 + 2 =
    22
    		 = 2
    4
    999

  1. If x = 3 + 2√2 , the value of x2 +
    1
    		 is
    x2








  1. View Hint View Answer Discuss in Forum

    x = 3 + 2√2

    ∴
    1
    		 =
    1
    x3 + 2√2

    =
    1
    		 ×
    3 − 2√2
    3 + 2√23 − 2√2

    =
    3 − 2√2
    9 − 8

    = 3 − 2√2
    x +
    1
    		 = 3 + 2√2 + 3 − 2√2 = 6
    x

    ∴ x2 +
    1
    		 = x +
    1
    		2 − 2
    x2x

    = (6)2 – 2 = 36 – 2 = 34

    Correct Option: D

    x = 3 + 2√2

    ∴
    1
    		 =
    1
    x3 + 2√2

    =
    1
    		 ×
    3 − 2√2
    3 + 2√23 − 2√2

    =
    3 − 2√2
    9 − 8

    = 3 − 2√2
    x +
    1
    		 = 3 + 2√2 + 3 − 2√2 = 6
    x

    ∴ x2 +
    1
    		 = x +
    1
    		2 − 2
    x2x

    = (6)2 – 2 = 36 – 2 = 34

  1. If a + b + c = 2s, then
    (s − a)2 + (s − b)2 + (s − c)2 + s2
    		 is equal to
    a2 + b2 + c2








  1. View Hint View Answer Discuss in Forum

    Expression =
    (s − a)2 + (s − b)2 + (s − c)2 + s2
    a2 + b2 + c2

    =
    s2 − 2sa + a2 + s2 + b2 − 2sb + s2 − 2sc + c2 + s2
    a2 + b2 + c2

    =
    4s2 + a2 + b2 + c2 − 2s(a + b + c)
    a2 + b2 + c2

    =
    4s2 + a2 + b2 + c2 − 4s2
    		 = 1
    a2 + b2 + c2

    Correct Option: C

    Expression =
    (s − a)2 + (s − b)2 + (s − c)2 + s2
    a2 + b2 + c2

    =
    s2 − 2sa + a2 + s2 + b2 − 2sb + s2 − 2sc + c2 + s2
    a2 + b2 + c2

    =
    4s2 + a2 + b2 + c2 − 2s(a + b + c)
    a2 + b2 + c2

    =
    4s2 + a2 + b2 + c2 − 4s2
    		 = 1
    a2 + b2 + c2

  1. If a, b, c are non-zero, a +
    1
    		 = 1 and b +
    1
    		 = 1, then the value of abc is :
    bc








  1. View Hint View Answer Discuss in Forum

    a +
    1
    		 = 1 ⇒ ab + 1 = b
    b

    ⇒  ab = b – 1       .....(i)
    Again,
    b +
    1
    		 = 1
    c

    1
    		 = 1 − b ⇒ c =
    1
    		       .....(ii)
    cb − c

    On multiplying (i) & (ii)
    abc =
    b − 1
    		 = − 1
    1 − b

    Correct Option: A

    a +
    1
    		 = 1 ⇒ ab + 1 = b
    b

    ⇒  ab = b – 1       .....(i)
    Again,
    b +
    1
    		 = 1
    c

    1
    		 = 1 − b ⇒ c =
    1
    		       .....(ii)
    cb − c

    On multiplying (i) & (ii)
    abc =
    b − 1
    		 = − 1
    1 − b

  1. If a + b + c = 0, then the value of
    a + b
    		 +
    b + c
    		 +
    c + a
    a
    		 +
    b
    		 +
    c
    		 is :
    cabb + cc + aa + b








  1. View Hint View Answer Discuss in Forum

    a + b + c = 0
    ⇒  a + b = – c ; b + c = – a , c + a = – b

    ∴ 
    a + b
    		 +
    b + c
    		 +
    c + a
    abc

    = – 1 – 1 – 1 = – 3
    a
    		 +
    b
    		 +
    c
    b + cc + aa + b

    = – 1 – 1 – 1 = – 3
    ∴  Expression = (– 3) × (– 3) = 9

    Correct Option: C

    a + b + c = 0
    ⇒  a + b = – c ; b + c = – a , c + a = – b

    ∴ 
    a + b
    		 +
    b + c
    		 +
    c + a
    abc

    = – 1 – 1 – 1 = – 3
    a
    		 +
    b
    		 +
    c
    b + cc + aa + b

    = – 1 – 1 – 1 = – 3
    ∴  Expression = (– 3) × (– 3) = 9