JEE Main & Advanced Mathematics Permutations and Combinations Question Bank

done Circular Permutations Total Questions - 14

• question_answer1)
  If eleven members of a committee sit at a round table so that the President and Secretary always sit together, then the number of arrangements is
  A)
  \[10\ !\ \times 2\] done clear
  B)
  \[10\,!\] done clear
  C)
  \[9\,!\ \times 2\] done clear
  D)
  None of these done clear
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• question_answer2)
  In how many ways can 5 keys be put in a ring
  A)
  \[\frac{1}{2}4!\] done clear
  B)
  \[\frac{1}{2}5\,!\] done clear
  C)
  \[4\,!\] done clear
  D)
  \[5\,!\] done clear
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• question_answer3)
  In how many ways can 5 boys and 5 girls sit in a circle so that no two boys sit together [IIT 1975; MP PET 1987]
  A)
  \[5!\,\times 5\,!\] done clear
  B)
  \[4\,!\,\,\times \,\,5\,!\] done clear
  C)
  \[\frac{5\,\,!\,\,\times \,\,5\,\,!}{2}\] done clear
  D)
  None of these done clear
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• question_answer4)
  In how many ways can 12 gentlemen sit around a round table so that three specified gentlemen are always together
  A)
  9 ! done clear
  B)
  10 ! done clear
  C)
  3 ! 10 ! done clear
  D)
  3 ! 9 ! done clear
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• question_answer5)
  In how many ways can 15 members of a council sit along a circular table, when the Secretary is to sit on one side of the Chairman and the Deputy Secretary on the other side
  A)
  \[2\times 12\,!\] done clear
  B)
  24 done clear
  C)
  \[2\times 15\,!\] done clear
  D)
  None of these done clear
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• question_answer6)
  In how many ways a garland can be made from exactly 10 flowers [MP PET 1984]
  A)
  \[10\ !\] done clear
  B)
  \[9\ !\] done clear
  C)
  \[2(9\ !)\] done clear
  D)
  \[\frac{9\ !}{2}\] done clear
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• question_answer7)
  20 persons are invited for a party. In how many different ways can they and the host be seated at a circular table, if the two particular persons are to be seated on either side of the host [IIT 1977]
  A)
  \[20\ !\] done clear
  B)
  \[2\ .\ 18\ !\] done clear
  C)
  \[18\ !\] done clear
  D)
  None of these done clear
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• question_answer8)
  The number of ways in which 5 beads of different colours  form a necklace is [RPET 2002]
  A)
  12 done clear
  B)
  24 done clear
  C)
  120 done clear
  D)
  60 done clear
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• question_answer9)
  \[n\] gentlemen can be made to sit on a round table in [MP PET 1982]
  A)
  \[\frac{1}{2}(n+1)\ !\] ways done clear
  B)
  \[(n-1)\ !\] ways done clear
  C)
  \[\frac{1}{2}(n-1)\ !\] ways done clear
  D)
  \[(n+1)\ !\] ways done clear
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• question_answer10)
  The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two female are not seated together is [Roorkee 1999]
  A)
  480 done clear
  B)
  600 done clear
  C)
  720 done clear
  D)
  840 done clear
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• question_answer11)
  In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together                               [EAMCET 1990; MP PET 2001; DCE 2001; UPSEAT 2002;Pb. CET 2000]
  A)
  \[{{(7\,!)}^{2}}\] done clear
  B)
  \[7\,!\,\times \,6\,!\] done clear
  C)
  \[{{(6\,!)}^{2}}\] done clear
  D)
  \[7\,!\] done clear
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• question_answer12)
  The number of circular permutations of n different objects is [Kerala (Engg.) 2001]
  A)
  n! done clear
  B)
  n done clear
  C)
  (n - 2)! done clear
  D)
  (n - 1)! done clear
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• question_answer13)
  The number of ways that 8 beads of different colours be string as a necklace is [EAMCET 2002]
  A)
  2520 done clear
  B)
  2880 done clear
  C)
  5040 done clear
  D)
  4320 done clear
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• question_answer14)
  The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by [AIEEE 2003; RPET 2003]
  A)
  6! × 5! done clear
  B)
  30 done clear
  C)
  5! × 4! done clear
  D)
  7! × 5! done clear
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