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Aptitude miscellaneous
  1. If x , y, and z are real numbers such that (x – 3)2 + (y – 4)2 + (z – 5)2 = 0 then, (x + y + z) is equal to








  1. View Hint View Answer Discuss in Forum

    If a2 + b2 + c2 = 0 then, a = 0, b = 0 and c = 0
    ∴ (x – 3)2 + (y – 4)2 + (z – 5)2 = 0
    ∴ x – 3 = 0 ⇒ x = 3
    y – 4 = 0 ⇒ y = 4
    z – 5 = 0 ⇒ z = 5
    ∴ x + y + z = 3 + 4 + 5 = 12

    Correct Option: D

    If a2 + b2 + c2 = 0 then, a = 0, b = 0 and c = 0
    ∴ (x – 3)2 + (y – 4)2 + (z – 5)2 = 0
    ∴ x – 3 = 0 ⇒ x = 3
    y – 4 = 0 ⇒ y = 4
    z – 5 = 0 ⇒ z = 5
    ∴ x + y + z = 3 + 4 + 5 = 12

  1. If (x – 4)(x2 + 4x + 42) = x3 - p, then p is equal to








  1. View Hint View Answer Discuss in Forum

    a3 – b3 = (a – b)(a2 + ab + b2)
    ∴ (x – 4)(x2 + 4x + 42) = x3 - 43 = x3 - 64
    ⇒ x3 - p = x3 - 64
    ⇒ p = 64

    Correct Option: C

    a3 – b3 = (a – b)(a2 + ab + b2)
    ∴ (x – 4)(x2 + 4x + 42) = x3 - 43 = x3 - 64
    ⇒ x3 - p = x3 - 64
    ⇒ p = 64

  1. The simplified value of 1 -
    2xy
    		 ÷
    x3 - y3
    		 - 3xy is
    x2 + y2x - y









  1. View Hint View Answer Discuss in Forum

    Expression = 1 -
    2xy
    		 ÷
    x3 - y3
    		 - 3xy
    x2 + y2x - y

    Expression =
    x2 + y2 - 2xy
    		 ÷
    (x - y)(x2 + xy + y2)
    		 - 3xy
    x2 + y2x - y

    Expression =
    (x - y)2
    		 ÷ (x2 + xy + y2 - 3xy)
    x2 + y2

    Expression =
    (x - y)2
    		 ÷ (x2 - 2xy + y2)
    x2 + y2

    Expression =
    (x - y)2
    		 ÷ (x - y)2
    x2 + y2

    Expression =
    1
    x2 + y2

    Correct Option: B

    Expression = 1 -
    2xy
    		 ÷
    x3 - y3
    		 - 3xy
    x2 + y2x - y

    Expression =
    x2 + y2 - 2xy
    		 ÷
    (x - y)(x2 + xy + y2)
    		 - 3xy
    x2 + y2x - y

    Expression =
    (x - y)2
    		 ÷ (x2 + xy + y2 - 3xy)
    x2 + y2

    Expression =
    (x - y)2
    		 ÷ (x2 - 2xy + y2)
    x2 + y2

    Expression =
    (x - y)2
    		 ÷ (x - y)2
    x2 + y2

    Expression =
    1
    x2 + y2

  1. If a + b + c = 0 then the value of
    1
    		 +
    1
    		 +
    1
    		 is
    (a + b)(b + c)(b + c)(c + a)(c + a)(a + b)









  1. View Hint View Answer Discuss in Forum

    1
    		 +
    1
    		 +
    1
    		 =
    c + a + a + b + b + c
    (a + b)(b + c)(b + c)(c + a)(c + a)(a + b)(a + b)(b + c)(c + a)

    1
    		 +
    1
    		 +
    1
    		 =
    2(a + b + c)
    		 = 0
    (a + b)(b + c)(b + c)(c + a)(c + a)(a + b)(a + b)(b + c)(c + a)

    Correct Option: A

    1
    		 +
    1
    		 +
    1
    		 =
    c + a + a + b + b + c
    (a + b)(b + c)(b + c)(c + a)(c + a)(a + b)(a + b)(b + c)(c + a)

    1
    		 +
    1
    		 +
    1
    		 =
    2(a + b + c)
    		 = 0
    (a + b)(b + c)(b + c)(c + a)(c + a)(a + b)(a + b)(b + c)(c + a)

  1. If x2 + y2 + 2x + 1 = 0, then the value of x31 + y35 is








  1. View Hint View Answer Discuss in Forum

    x2 + y2 + 2x + 1 = 0
    ⇒ x2 + 2x + 1 + y2 = 0
    ⇒ (x + 1)2 + y2 = 0
    ∴ x + 1 = 0 ⇒ x = –1 and y = 0
    ∴ x31 + y35 = (-1)31 + 0 = -1

    Correct Option: A

    x2 + y2 + 2x + 1 = 0
    ⇒ x2 + 2x + 1 + y2 = 0
    ⇒ (x + 1)2 + y2 = 0
    ∴ x + 1 = 0 ⇒ x = –1 and y = 0
    ∴ x31 + y35 = (-1)31 + 0 = -1