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  • Question
  • In how many ways can the letters of the word 'Director' be arranged so that the three vowels are never together?


  • Options
  • A. 1800
  • B. 18000
  • C. 16000
  • D. 1600

  • Correct Answer
  • 18000 

    Explanation

    Total number of letters = 8
    Number of vowels = 3 and r occurs twice.
    Total number of arrangements when there is no restriction = 8!/2!

    When three vowels are together, regarding them as one letter, we have only 5 + 1 = 6 letters
    These six letters can be arranged in 6!/2! ways, since r occurs twice.
    But the three vowels can be arranged among themselves in 3! ways.
    Hence number of arrangement when the three vowels are together = 6! /(2 !x 3!)

    ? Required number = 8!/2! - {6! / (2! x 3!)} = 18,000


  • More questions

    • 1. 
      A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speed is?

    • Options
    • A. 4:1
    • B. 1.4
    • C. 2:1
    • D. 1:2
    • Discuss
    • 2. 
      The length of the train that takes 8 second to pass a pole where it runs at a speed of 36 km/hr is?

    • Options
    • A. 288 meters
    • B. 45 meters
    • C. 48 meters
    • D. 80 meters
    • Discuss
    • 3. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

    • Options
    • A. 12 sec
    • B. 24 sec
    • C. 48 sec
    • D. 60 sec
    • Discuss
    • 4. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

    • Options
    • A. 3.6 sec
    • B. 18 sec
    • C. 36 sec
    • D. 72 sec
    • Discuss
    • 5. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

    • Options
    • A. 48 km/hr
    • B. 54 km/hr
    • C. 66 km/hr
    • D. 82 km/hr
    • Discuss
    • 6. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

    • Options
    • A. 9 a.m.
    • B. 10 a.m.
    • C. 10.30 a.m.
    • D. 11 a.m.
    • Discuss
    • 7. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

    • Options
    • A. 12 sec
    • B. 24 sec
    • C. 48 sec
    • D. 60 sec
    • Discuss
    • 8. When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

    • Options
    • A. Rs. 21,000
    • B. Rs. 22,500
    • C. Rs. 25,300
    • D. Rs. 25,800
    • Discuss
    • 9. If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y =?

    • Options
    • A. 2 or 6
    • B. 4
    • C. 4 or 8
    • D. 8
    • E. None of these
    • Discuss
    • 10. The difference of the squares of two consecutive odd integers is divisible by which of the following integers?

    • Options
    • A. 3
    • B. 6
    • C. 7
    • D. 8
    • Discuss


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