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  • Question
  • In an examination, 30% of the total students failed in Hindi, 45% failed in English and 20% failed in both the subjects. Find the percentage of those who passed in both the subjects.


  • Options
  • A. 35.7%
  • B. 35%
  • C. 40%
  • D. 45%

  • Correct Answer
  • 45% 

    Explanation

    Let the number of students be 100. Number of students who failed in Hindi is 30%.
    n(H) = 30
    Number of students who failed in English is 45%.
    ? n(E) = 45
    Number of students who failed in both the subjects is 20%. n(H ? E) = 20
    Applying the rule,
    n(H ? E) = n(H) + n(E) - n(H ? E)
    = 30 + 45 - 20 = 55
    Percentage of students who failed in Hindi or English or both the subjects = 55%
    Number of students who passed in both the subjects = 100 - 55 = 45%


  • Sets and Functions problems


    Search Results


    • 1. 
      There are 80 families in a small extension area. 20 per cent of these families own a car each. 50 per cent of the remaining families own a motor cycle each. How many families in that extension do not own any vehicle?

    • Options
    • A. 30
    • B. 32
    • C. 23
    • D. 36
    • Discuss
    • 2. 
      In a group of 50 people, 35 speak Hindi, 25 speak both Hindi and English and all the people speak Hindi or English or both. The number of people who speak English only is:

    • Options
    • A. 40
    • B. 20
    • C. 15
    • D. 10
    • Discuss
    • 3. 
      If A = {1, 2, 3}, B = {2, 3, 4}, C = {1, 3, 4} and D = {2, 4, 5}, then (A × B) ? (C × D) =?

    • Options
    • A. (A ? D) × (B ? C)
    • B. (b) (A ? C) × (B ? D)
    • C. ?
    • D. None of these
    • Discuss
    • 4. 
      If A = {a, d}, B = {b, c, e} and C = {b, c, f}, then A × (B - C) =

    • Options
    • A. (A × B) - (A × C)
    • B. (A × B)
    • C. A × C
    • D. None of these
    • Discuss
    • 5. 
      If A = {a, d}, B = {b, c, e} and C = {b, c, f}, then A × (B ? C) =


    • Options
    • A. ?
    • B. (A × B) ? (A × C)
    • C. (A × B) ? (A × C)
    • D. None of these
    • Discuss
    • 6. 
      If A = {1, 2, 3, 4, 5} and B = {2, 4, 6} then what is the value of A - B?

    • Options
    • A. {2, 3, 5}
    • B. {1, 3, 5}
    • C. {2, 3, 6}
    • D. {1, 4, 5}
    • Discuss
    • 7. 
      Write down the power set of A = {8, 9}.

    • Options
    • A. {?, {8}, {9}, {8, 9}}
    • B. {?, {8}, {9}}
    • C. {?, {8}, {9}, {8, 9}}
    • D. None of these
    • Discuss
    • 8. 
      Which of the following pairs of sets are comparable?

    • Options
    • A. A = {1, 3, 5}, and B = {3, 2, 5, 6}
    • B. A = {x: x ? N and x ? 10} and B = {1, 2, 3,?, 10, 11}
    • C. A = {1, 2, 3, {4, 5}}, and B = {1, 2, 3, 4, 5}.
    • D. None of these
    • Discuss
    • 9. 
      In a class, 50 students play cricket, 20 students play football and 10 play both cricket and football. How many play at least one of these two games?

    • Options
    • A. 60
    • B. 45
    • C. 55
    • D. 65
    • Discuss
    • 10. 
      Which of the following sets is finite?

    • Options
    • A. {x: x ? N and x is a prime number}
    • B. {x: x is a quadrilateral on a plane}
    • C. {x: x ? N and x2 ? 25 ? 0}
    • D. {x: x ? N and x is a multiple of 3}
    • Discuss


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