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Aptitude miscellaneous
  1. If x * y = x2 + y2 – xy, then the value of 9 * 11 is








  1. View Hint View Answer Discuss in Forum

    x * y = x2 + y2 – xy (Given)
    ⇒  9 * 11 = 92 + 112 – 9 × 11
    = 81 + 121 – 99
    = 202 – 99 = 103

    Correct Option: B

    x * y = x2 + y2 – xy (Given)
    ⇒  9 * 11 = 92 + 112 – 9 × 11
    = 81 + 121 – 99
    = 202 – 99 = 103

  1. If   47.2506 = 4A +
    7
    		 + 2C +
    5
    		 + 6E ,
    BD
    then the value of 5A + 3B + 6C + D + 3E is








  1. View Hint View Answer Discuss in Forum

    4A +
    7
    		 + 2C +
    5
    		 + 6E = 47.2506
    BD

    = 40 + 7 +
    2
    		 +
    5
    		 +
    6
    1010010000

    4A = 40 ⇒ A = 10
    7
    		 = 7 ⇒ 7B = 7 = ⇒ B = 1
    B

    2 C =
    2
    		 ⇒ C = 0.1
    10

    5
    		 =
    5
    		 ⇒ D = 100
    D100

    6E =
    6
    		 ⇒ E = 0.0001
    10000

    5A + 3B + 6C + D + 3E
    = 5 × 10 + 3 × 1 + 6 × 0.1 + 100 + 3 × 0.0001
    = 50 + 3 + 0.6 + 100 + 0.0003
    = 153.6003

    Correct Option: C

    4A +
    7
    		 + 2C +
    5
    		 + 6E = 47.2506
    BD

    = 40 + 7 +
    2
    		 +
    5
    		 +
    6
    1010010000

    4A = 40 ⇒ A = 10
    7
    		 = 7 ⇒ 7B = 7 = ⇒ B = 1
    B

    2 C =
    2
    		 ⇒ C = 0.1
    10

    5
    		 =
    5
    		 ⇒ D = 100
    D100

    6E =
    6
    		 ⇒ E = 0.0001
    10000

    5A + 3B + 6C + D + 3E
    = 5 × 10 + 3 × 1 + 6 × 0.1 + 100 + 3 × 0.0001
    = 50 + 3 + 0.6 + 100 + 0.0003
    = 153.6003

  1. Given that 100.48 = x, 100.70 = y, and xz = y2 , then the value of z is close to








  1. View Hint View Answer Discuss in Forum

    We have,
    100.48 = x, 100.70 = y
    ∴  xz = y2
    ⇒  (100.48)z = (100.70)2
    ⇒  100.48z = 101.4
    ⇒  0.48z = 1.4

    ⇒  z =
    1.4
    		 = 2.9
    0.48

    Correct Option: C

    We have,
    100.48 = x, 100.70 = y
    ∴  xz = y2
    ⇒  (100.48)z = (100.70)2
    ⇒  100.48z = 101.4
    ⇒  0.48z = 1.4

    ⇒  z =
    1.4
    		 = 2.9
    0.48

  1. If a ⊗ b = (a × b) + b, then 5 ⊗ 7 equals to








  1. View Hint View Answer Discuss in Forum

    It is given that
    a ⊗ b = (a × b) + b
    ∴  5 ⊗ 7 = (5 × 7) + 7 = 35 + 7 = 42

    Correct Option: C

    It is given that
    a ⊗ b = (a × b) + b
    ∴  5 ⊗ 7 = (5 × 7) + 7 = 35 + 7 = 42

  1. If 1 < x < 2, then the value of √(x − 1)2 + √(x − 3)2 is








  1. View Hint View Answer Discuss in Forum

    Since 1 < x < 2, we have
    x – 1 > 0 and
    x – 3 < 0
    or, 3 – x > 0
    ∴  √(x − 1)2 + √(x − 3)2
    = √(x − 1)2 + √(3 − x)2
    [∴  (x − 3)2 = (3 – x)2]
    = x – 1 + 3 – x = 2

    Correct Option: B

    Since 1 < x < 2, we have
    x – 1 > 0 and
    x – 3 < 0
    or, 3 – x > 0
    ∴  √(x − 1)2 + √(x − 3)2
    = √(x − 1)2 + √(3 − x)2
    [∴  (x − 3)2 = (3 – x)2]
    = x – 1 + 3 – x = 2