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PREVIOUS YEAR SOLVED PAPERS - GATE 2019

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6. The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements:
P says “Q committed the crime.”
Q says “S committed the crime.”
R says “ I did not do it.”
S says “What Q said about me is false”.
Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?

  • Option : B
  • Explanation : Case I:
     CriminalsPQRS
     AssumptionFTFF
     ResultQNCSCRCSC

    S and R are criminal in the result is impossible because only one person committed the crime.
    Case II:
     CriminalsPQRS
     AssumptionTFFF
     ResultQCSNCRCSC

    Q and R are criminal in the result is impossible because only one person committed the crime.
    Case III:
     CriminalsPQRS
     AssumptionFFTF
     ResultQNCSNCRNCSC

    SNC and SC in the result which is contradiction. [S committed crime and same time not committed crime which is contradiction]
    Case IV:
     CriminalsPQRS
     AssumptionFFFT
     ResultQNCSNCRCSNC

    R is criminal in the result.
    Hence this case satisfies only one person committed the crime.
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7. In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. Out of the total number of the people, the percentage of administrators shall be in the range of ___________.

  • Option : C
  • Explanation :
    Percentage of Administrators = (Administrator/Total) x 100
                  =(50/60) x 100 = 31.25
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8. “A recent High Court judgement has sought to dispel the idea of begging as a disease — which leads to its stigmatization and criminalization — and to regard it as a symptom. The underlying disease is the failure of the state to protect citizens who fall through the social security net.”
Which one of the following statements can be inferred from the given passage?

  • Option : B
  • Explanation :
    The passage states that the underlying disease behind begging is the failure of the state to protect citizens who fall through the social security net.
    option B can be concluded from the above.
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9. In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths clubs, and 2 students are in all the clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is ___________.

  • Option : C
  • Explanation :

    Total number of students = 60 + 80 + 30 + 38 + 5 + 10 + 2 = 225
    25% = 225
    100% = (225/25) x 100 = 900
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10. Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vacant rooms, select the allocation plan that will accommodate all their requests.
Request by X: Due to pollen allergy, I want to avoid a wing next to the garden.
Request by Y: I want to live as far from the washrooms as possible, since I am very sensitive to smell.
Request by Z: I believe in Vaastu and so want to stay in the South-west wing.
The shaded rooms are already occupied. WR is washroom

  • Option : D
  • Explanation :
    In all other option except D, Z is not staying in south-west wing. Since Z believe in vastu, he can stay in Any of the south-west wings but not in any other wing. In option (D) X is away from the garden as well as Y is away from the washroom. So, option (D) is correct.
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GATE 2019