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  • Question
  • A five-digit number divisible by 3 is to be formed using digits 0, 1, 2, 3, 4 and 5 without repetition, the total number of ways this can be done, is


  • Options
  • A. 122
  • B. 210
  • C. 216
  • D. 217

  • Correct Answer
  • 216 

    Explanation

    A five-digit number, which is divisible by 3, is formed when sum of digits is also divisible by 3.

    So, combination formed using six-digits, which are divisible by 3
    = 5 + 4 + 3 + 2 + 1 = 15
    = 5 + 4 + 2 + 1 + 0 = 12

    So, set of number are (5, 4, 3, 2, 1) and (5, 4, 2, 1, 0).

    Number formed by using 1st set = 5 x 4 x 3 x 2 x 1 = 120
    Similarly, using 2nd set = 4 x 4 x 3 x 2 x 1 = 96

    Hence, using 2nd set, underlined place cannot be filled by 0, otherwise it will become a four-digit number.
    ? Total number = 120 + 96 = 216


  • Permutation and Combination problems


    Search Results


    • 1. 
      The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a group consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee if Mr. Y is its member, is

    • Options
    • A. 1960
    • B. 3240
    • C. 1540
    • D. None of these
    • Discuss
    • 2. 
      There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities, is

    • Options
    • A. 92
    • B. 90
    • C. 91
    • D. 93
    • Discuss
    • 3. 
      A question paper consists of two sections having respectively 3 and 5 questions. The following note is given on the paper. "It is not necessary to attempt all the question". One question from each section is compulsory. In how many ways, a candidate can select the question?

    • Options
    • A. 38
    • B. 217
    • C. 256
    • D. 320
    • Discuss
    • 4. 
      There are 14 points in a plane, out of which 4 are collinear. Find the number of triangles made by these points .

    • Options
    • A. 364
    • B. 360
    • C. 368
    • D. 365
    • Discuss
    • 5. 
      In how many ways, can 24 persons be seated around a circular table if there are is 13 seats?

    • Options
    • A. 24! / [13 x 11! ]
    • B. 22! / [14 x 12!]
    • C. 23! / [13 x 11!]
    • D. 24! / [12 x 12!]
    • Discuss
    • 6. 
      A new flag is to be designed with six vertical stripes using some or all of the colour yellow, green,blue and red. Then, the number of ways this can be made such that no two adjacent stripes have the same colour is

    • Options
    • A. 12 x 81
    • B. 16 x 192
    • C. 20 x 125
    • D. 24 x 216
    • Discuss
    • 7. 
      An intelligence agency forms a code of two distinct digits selected from 0, 1, 2,....., 9 such that the first-digit of code is non-zero. The code, handwritten on a slip, can however potentially create confusion when read upside down, for examples the code 91 may appear as 16. how many codes are there for which no such confusion can arise?

    • Options
    • A. 80
    • B. 78
    • C. 71
    • D. 69
    • Discuss
    • 8. 
      How many numbers can be formed from 1, 2, 3, 4, 5, ( without repetition), when the digit at the unit's place must be greater than that in the ten's place?

    • Options
    • A. 54
    • B. 60
    • C. 51/3
    • D. 2 x 4!
    • Discuss
    • 9. 
      Boxes numbered 1, 2, 3, 4, and 5 are kept in a row and they are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then, how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?

    • Options
    • A. 8
    • B. 10
    • C. 15
    • D. 22
    • Discuss
    • 10. 
      Marks obtained by an student in 5 subjects are given below 25, 26, 27, 28, 29 in these obtained marks 27 is

    • Options
    • A. mode
    • B. median and mode
    • C. mean and median
    • D. both (a) and (c)
    • Discuss


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