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Aptitude miscellaneous
  1. The maximum value of 5 + 20x – 4x2 , when x is a real number is :








  1. View Hint View Answer Discuss in Forum

    For y = ax2 + bx + c

    Maximum value = c –
    b2
    4a

    Here, c = 5, b = 20, a = –4
    ∴ Maximum value = 5 –
    20 × 20
    		 = 5 + 5 × 5 = 30
    4 × −4

    Correct Option: D

    For y = ax2 + bx + c

    Maximum value = c –
    b2
    4a

    Here, c = 5, b = 20, a = –4
    ∴ Maximum value = 5 –
    20 × 20
    		 = 5 + 5 × 5 = 30
    4 × −4

  1. If  
    1
    		(a − b)2+ ab = p (a + b)2 ,then the value of p is :
    2








  1. View Hint View Answer Discuss in Forum

    1
    		(a − b)2+ ab = p (a + b)2
    2

    ⇒ 
    1
    		(a2 + b2 − 2ab) + ab = p (a + b)2
    4

    ⇒ 
    1
    		(a2 + b2 − 2ab + 4ab) = p (a + b)2
    4

    ⇒ 
    1
    		(a + b)2 = p (a + b)2
    4

    ⇒  p =
    1
    4

    Correct Option: C

    1
    		(a − b)2+ ab = p (a + b)2
    2

    ⇒ 
    1
    		(a2 + b2 − 2ab) + ab = p (a + b)2
    4

    ⇒ 
    1
    		(a2 + b2 − 2ab + 4ab) = p (a + b)2
    4

    ⇒ 
    1
    		(a + b)2 = p (a + b)2
    4

    ⇒  p =
    1
    4

  1. If a +
    1
    		2 = 3, then the value of a2 +
    1
    		 will be
    aa2








  1. View Hint View Answer Discuss in Forum

    a +
    1
    		2 = 3
    a

    ⇒  a2 +
    1
    		+ 2 = 3
    a2

    ⇒  a2 +
    1
    		 = 3 − 2 = 1
    a2

    Correct Option: B

    a +
    1
    		2 = 3
    a

    ⇒  a2 +
    1
    		+ 2 = 3
    a2

    ⇒  a2 +
    1
    		 = 3 − 2 = 1
    a2

  1. If (a + b – 6)2 + a2 + b2 + 1 + 2b = 2ab + 2a, then the value of a is








  1. View Hint View Answer Discuss in Forum

    (a + b – 6)2 + a2 + b2 + 1 + 2b = 2ab + 2a
    ⇒  (a + b – 6)2 + a2 + b2 +1 + 2b – 2ab – 2a = 0
    ⇒  (a + b – 6)2 + (a)2 + (–b)2 + (–1)2 + 2a (–b) + 2 (–b) (–1) + 2 (a) (–1) = 0
    ⇒  (a + b – 6)2 + (a – b – 1)2 = 0
    ⇒  a + b – 6 = 0 and a – b – 1 = 0
    ⇒  a + b = 6 and a – b = 1
    On adding these two equations,
    a + b + a – b = 6 + 1
    ⇒  2a = 7

    ⇒  a =
    7
    		 = 3.5
    2

    Correct Option: C

    (a + b – 6)2 + a2 + b2 + 1 + 2b = 2ab + 2a
    ⇒  (a + b – 6)2 + a2 + b2 +1 + 2b – 2ab – 2a = 0
    ⇒  (a + b – 6)2 + (a)2 + (–b)2 + (–1)2 + 2a (–b) + 2 (–b) (–1) + 2 (a) (–1) = 0
    ⇒  (a + b – 6)2 + (a – b – 1)2 = 0
    ⇒  a + b – 6 = 0 and a – b – 1 = 0
    ⇒  a + b = 6 and a – b = 1
    On adding these two equations,
    a + b + a – b = 6 + 1
    ⇒  2a = 7

    ⇒  a =
    7
    		 = 3.5
    2

  1. If   x + 3y = – 3x + y, then
    x2
    		   is equal to
    2y2








  1. View Hint View Answer Discuss in Forum

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

    ⇒ 
    x
    		 = −
    1
    y2

    ∴ 
    x2
    		 = −
    1
    		2
    y22

    =
    1
    4

    ∴ 
    x2
    		 =
    1
    		 ×
    1
    		 =
    1
    2y2248

    Correct Option: A

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

    ⇒ 
    x
    		 = −
    1
    y2

    ∴ 
    x2
    		 = −
    1
    		2
    y22

    =
    1
    4

    ∴ 
    x2
    		 =
    1
    		 ×
    1
    		 =
    1
    2y2248