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Quiz: Permutations and Combinations

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Number of Questions: 40

Question: 21 -

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together? 

Options:

  1. None of these

  2. 4989600

  3. 120960

  4. 10080

    5. Answer:

    120960
    Solution:

    In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.

    Thus, we have MTHMTCS (AEAI).

    Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.

    Number of ways of arranging these letters = 8! = 10080.
    (2!)(2!)

    Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

    Number of ways of arranging these letters = 4! = 12.
    2!

    Required number of words = (10080 x 12) = 120960.

Question: 22 -

A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most 

Options:

  1. 216

  2. 243

  3. 214

  4. 215

    5. Answer:

    215
    Solution:

    Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
    Maximum number of unsuccessful attempts = 216 - 1 = 215.

Question: 23 -

A locker in bank has 3 digit lock. Mahesh forgot his password and was trying all possible combinations. He took 6 seconds for each try. The problem was that each digit can be from 0 to 9. How much time will be needed to by Mahesh to try all the combinations?

Options:

  1. 120 minutes

  2. 90 minutes

  3. 100 minutes

  4. 60 minutes

    5. Answer:

    100 minutes
    Solution:

    permutation and combination

Question: 24 -

Mayur travels from Mumbai to Jammu in 7 different ways. But he is allowed to return to Mumbai by any way except the one he used earlier. In how many ways can he complete his journey?

Options:

  1. 42

  2. 48

  3. 6

  4. 49

    5. Answer:

    42
    Solution:

    permutation and combination

Question: 25 -

 In Daya’s bag there are 3 books of History, 4 books of Science and 2 books of Maths. In how many ways can Daya arrange the books so that all the books of same subject are together?

Options:

  1. 6

  2. 1728

  3. 9

  4. 8640

    5. Answer:

    1728
    Solution:

    permutation and combination