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Aptitude miscellaneous
  1. If  
    a
    		 =
    25
    		 , then the value of
    a2 − b2
    		 is
    b6a2 + b2








  1. View Hint View Answer Discuss in Forum

    a
    		 =
    25
    b6

    ⇒ 
    a2
    		 =
    252
    b262

    =
    625
    36

    By componendo and dividendo,
    a2 − b2
    		 =
    625 − 36
    a2 + b2625 + 36

    =
    589
    661

    Correct Option: A

    a
    		 =
    25
    b6

    ⇒ 
    a2
    		 =
    252
    b262

    =
    625
    36

    By componendo and dividendo,
    a2 − b2
    		 =
    625 − 36
    a2 + b2625 + 36

    =
    589
    661

  1. If   x + y = 2a, then the value of
    a
    		 +
    a
    		 is
    x − ay − a








  1. View Hint View Answer Discuss in Forum

    x + y = 2a = a + a
    ⇒  x – a = a – y

    Expression =
    a
    		 +
    a
    x − ay − a

    =
    a
    		 −
    a
    x − aa − y

    =
    a
    		 −
    a
    		 = 0
    x − ax − a

    Correct Option: B

    x + y = 2a = a + a
    ⇒  x – a = a – y

    Expression =
    a
    		 +
    a
    x − ay − a

    =
    a
    		 −
    a
    x − aa − y

    =
    a
    		 −
    a
    		 = 0
    x − ax − a

  1. If a2 + b2 + c2 = ab + bc + ca,
    then the value of
    a + c
    		is
    b








  1. View Hint View Answer Discuss in Forum

    a2 + b2 + c2 = ab + bc + ca
    ⇒  2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca = 0
    ⇒  a2 + b2 – 2ab + b2 + c2 – 2bc + c2 + a2 – 2ca = 0
    ⇒  (a – b)2 + (b – c)2 + (c – a)2 = 0
    ⇒  a – b = 0, b – c = 0, c – a = 0
    ⇒  a = b, b = c, c = a
    ⇒  a = b = c

    ∴ 
    a + c
    		 =
    2a
    		 = 2
    ba

    Correct Option: B

    a2 + b2 + c2 = ab + bc + ca
    ⇒  2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca = 0
    ⇒  a2 + b2 – 2ab + b2 + c2 – 2bc + c2 + a2 – 2ca = 0
    ⇒  (a – b)2 + (b – c)2 + (c – a)2 = 0
    ⇒  a – b = 0, b – c = 0, c – a = 0
    ⇒  a = b, b = c, c = a
    ⇒  a = b = c

    ∴ 
    a + c
    		 =
    2a
    		 = 2
    ba

  1. If (x – 2) is a factor of x2 + 3Qx – 2Q, then the value of Q is








  1. View Hint View Answer Discuss in Forum

    P(x) = x2 + 3Qx – 2Q
    ∵  (x – 2) is a factor of P(x).
    ∴  P(2) = 0
    ⇒  (2)2 + 3Q × 2 – 2Q = 0
    ⇒  4 + 6Q – 2Q = 0
    ⇒  4Q + 4 = 0
    ⇒  4Q = – 4 ⇒ Q = –1

    Correct Option: D

    P(x) = x2 + 3Qx – 2Q
    ∵  (x – 2) is a factor of P(x).
    ∴  P(2) = 0
    ⇒  (2)2 + 3Q × 2 – 2Q = 0
    ⇒  4 + 6Q – 2Q = 0
    ⇒  4Q + 4 = 0
    ⇒  4Q = – 4 ⇒ Q = –1

  1. If x + y + z = 13 and x2 + y2 + z2 = 69, then xy + z (x + y) is equal
    to








  1. View Hint View Answer Discuss in Forum

    x + y + z = 13
    x2 + y2 + z2 = 69
    (x + y + z)2
    = x2 + y2 + z2 +2 (xy + yz + zx)
    ⇒  (13)2 = 69 + 2 (xy + yz + zx)
    ⇒  2 (xy + yz + zx)
    = 169 – 69 = 100

    ⇒  xy + yz + zx =
    100
    		 = 50
    2

    Correct Option: C

    x + y + z = 13
    x2 + y2 + z2 = 69
    (x + y + z)2
    = x2 + y2 + z2 +2 (xy + yz + zx)
    ⇒  (13)2 = 69 + 2 (xy + yz + zx)
    ⇒  2 (xy + yz + zx)
    = 169 – 69 = 100

    ⇒  xy + yz + zx =
    100
    		 = 50
    2