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Aptitude miscellaneous
  1. If
    a
    		 +
    b
    		 = 1, then the value of (a³ + b³) is :
    ba








  1. View Hint View Answer Discuss in Forum

    a
    		 +
    b
    		 = 1
    ba

    ⇒
    a² + b²
    		 = 1
    ab

    ⇒ a² + b² = ab
    ⇒ a² – ab + b² = 0
    ∴ a³ + b³ = (a + b) (a² – ab + b²) = 0

    Correct Option: B

    a
    		 +
    b
    		 = 1
    ba

    ⇒
    a² + b²
    		 = 1
    ab

    ⇒ a² + b² = ab
    ⇒ a² – ab + b² = 0
    ∴ a³ + b³ = (a + b) (a² – ab + b²) = 0

  1. If (a + b) = 5, then the value of (a – 3)7 + (b – 2)7 is :








  1. View Hint View Answer Discuss in Forum

    a + b = 5
    ⇒ a – 3 = 2 – b
    ⇒ (a – 3)7 = (2 – b)7
    ⇒ (a – 3)7 = – (b – 2)7
    ⇒ (a – 3)7 + (b – 2)7 = 0

    Correct Option: D

    a + b = 5
    ⇒ a – 3 = 2 – b
    ⇒ (a – 3)7 = (2 – b)7
    ⇒ (a – 3)7 = – (b – 2)7
    ⇒ (a – 3)7 + (b – 2)7 = 0

  1. If (x² – 2x + 1) = 0, then the value ofx4 +
    1
    		is :
    x4








  1. View Hint View Answer Discuss in Forum

    x² – 2x + 1 = 0
    ⇒ (x – 1)² = 0
    ⇒ x – 1 = 0
    ⇒ x = 1

    ∴ x4 +
    1
    		 = 1 + 1 = 2
    x4

    Correct Option: C

    x² – 2x + 1 = 0
    ⇒ (x – 1)² = 0
    ⇒ x – 1 = 0
    ⇒ x = 1

    ∴ x4 +
    1
    		 = 1 + 1 = 2
    x4

  1. If a²+ b² + c² = 83 and a + b + c = 15, then the value of (ab + bc + ca) is :








  1. View Hint View Answer Discuss in Forum

    a² + b² + c² = 83
    a + b + c = 15
    ∴ (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
    ⇒ (15)² = 83 + 2 (ab + bc + ca)
    ⇒ 225 – 83 = 2(ab + bc + ca)
    ⇒ 142 = 2 (ab + bc + ca)
    ⇒ ab + bc + ca = 142/2
    = 71

    Correct Option: C

    a² + b² + c² = 83
    a + b + c = 15
    ∴ (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
    ⇒ (15)² = 83 + 2 (ab + bc + ca)
    ⇒ 225 – 83 = 2(ab + bc + ca)
    ⇒ 142 = 2 (ab + bc + ca)
    ⇒ ab + bc + ca = 142/2
    = 71

  1. If m – n = 2 and mn = 15, (m, n > 0) then the value of (m² – n²) (m³ – n³) is :








  1. View Hint View Answer Discuss in Forum

    m – n = 2; mn = 15
    ∴ (m + n)² = (m – n)² + 4mn = 4 + 4 × 15 = 64
    ⇒ m + n = 64 = 8
    ∴ m + n + m – n = 8 + 2 = 10
    ⇒ 2m = 10 ⇒ m = 5
    ∴ m + n = 8 ⇒ 5 + n = 8
    ⇒ n = 8 – 5 = 3
    ∴ (m² – n²) (m³ – n³)
    = (5² – 3²) (5³ – 3³)
    = (25 – 9) (125 – 27)
    = 16 × 98 = 1568

    Correct Option: D

    m – n = 2; mn = 15
    ∴ (m + n)² = (m – n)² + 4mn = 4 + 4 × 15 = 64
    ⇒ m + n = 64 = 8
    ∴ m + n + m – n = 8 + 2 = 10
    ⇒ 2m = 10 ⇒ m = 5
    ∴ m + n = 8 ⇒ 5 + n = 8
    ⇒ n = 8 – 5 = 3
    ∴ (m² – n²) (m³ – n³)
    = (5² – 3²) (5³ – 3³)
    = (25 – 9) (125 – 27)
    = 16 × 98 = 1568