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Home ‣ Aptitude ‣ Linear Equation See What Others Are Saying!
  • Question

  • The graph of ax + by = c, dx + ey = f will be
    I. parallel, if the system has no solution.
    II. coincident, if the system has finite number of solutions.
    III. intersecting. if the system has only one solution.
    Which of the above statements are correct?


  • Options
  • A. Only I and II
  • B. Only II and II
  • C. Only I and III
  • D. I, II and III

  • Correct Answer
  • Only I and III 

    Explanation

    ax + by = c and dx + ey = f
    a1/a2 = a/d, b1/b2 = b/e, c1/c2 = c/f
    ? b1/b2 ? c1/c2
    ? b/e ? c/f
    it represent a pair of parallel lines.
    ? a1/a2 ? b1/b2
    ? a/d ? b/e
    Therefore, system has unique solutions and represents a pair of intersecting lines.

    • More questions

    • 1. 
      The value of (0.96)3 - (0.1)3 is:
      (0.96)2 + 0.096 + (0.1)2

    • Options
    • A. 0.86
    • B. 0.95
    • C. 0.97
    • D. 1.06
      • Discuss
    • 2. 
      A man has given one-fourth part of his property to his daughter, half part to his sons and one-fifth part given as charity. How much part of his property he has given?

    • Options
    • A. 1/20
    • B. 19/20
    • C. 1/10
    • D. 9/10
      • Discuss
    • 3. 
      When a 192 meters long rod is cut down into small pieces of length 3·2 meters each. Then how many pieces are available?

    • Options
    • A. 52
    • B. 68
    • C. 62
    • D. None of these
      • Discuss
    • 4. 
      If a * b = a + b + a/b, Then the value of 12 * 4 is

    • Options
    • A. 48
    • B. 19
    • C. 20
    • D. 21
      • Discuss
    • 5. 
      When A alone does a piece of work, he takes 25 days more than the time taken by (A + B) to complete that particular work, while B alone takes 49 days more than the time taken by (A + B) to finish the same work . A and B together will take what time for finish this work?

    • Options
    • A. 35 days
    • B. 25 days
    • C. 15 days
    • D. 45 days
      • Discuss
    • 6. 
      If the rate of interest rises from 6 1/2 to 8% a man's annual income increases by Rs. 4050. Find the capital.

    • Options
    • A. Rs . 270000
    • B. Rs . 370000
    • C. Rs . 300000
    • D. None of these
      • Discuss
    • 7. 16, 33, 65, 131, 261, (....)

    • Options
    • A. 523
    • B. 521
    • C. 613
    • D. 721
      • Discuss
    • 8. 
      16.7 + 12.38 -? =10.09

    • Options
    • A. 17.89
    • B. 18.99
    • C. 16.98
    • D. 20.09
      • Discuss
    • 9. 
      A mixture of 20 kg of spirit and water contains 10 % water. How much water must be added to this mixture to raise the percentage of water to 25 %?

    • Options
    • A. 4 kg
    • B. 5 kg
    • C. 8 kg
    • D. 30 kg
      • Discuss
    • 10. 
      A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time.
      If he had not engaged the additional men, how many days behind schedule would it be finished?

    • Options
    • A. 7
    • B. 18
    • C. 12
    • D. None
      • Discuss

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