JEE Main & Advanced Mathematics Permutations and Combinations Question Bank

done Mock Test - Permutations and Combinations Total Questions - 25

• question_answer1)
  Total number of six-digit numbers that can be formed having the property that every succeeding digit is greater than the preceding digit is equal to
  A)
  \[^{9}{{C}_{3}}\]                  done clear
  B)
  \[^{10}{{C}_{3}}\] done clear
  C)
  \[^{9}{{P}_{3}}\]                   done clear
  D)
  \[^{10}{{P}_{3}}\] done clear
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• question_answer2)
  In a room, there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amount of illumination is
  A)
  \[{{12}^{2}}-1\]         done clear
  B)
  \[{{2}^{12}}\] done clear
  C)
  \[{{2}^{12}}-1\]         done clear
  D)
  \[{{12}^{2}}\] done clear
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• question_answer3)
  Total number less than 3 x \[{{10}^{8}}\] and can be formed using the digits 1,2,3 is equal to
  A)
  \[\frac{1}{2}({{3}^{9}}+4\times {{3}^{8}})\] done clear
  B)
  \[\frac{1}{2}({{3}^{9}}-3)\] done clear
  C)
  \[\frac{1}{2}(7\times {{3}^{8}}-3)\]     done clear
  D)
  \[\frac{1}{2}({{3}^{9}}-3+{{3}^{8}})\] done clear
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• question_answer4)
  The number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is
  A)
  \[{{105}^{5}}\]          done clear
  B)
  \[210\times 243\] done clear
  C)
  \[105\times 243\]           done clear
  D)
  \[150\times {{21}^{2}}\] done clear
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• question_answer5)
  The number of ways to fill each of the four cells of the table with a distinct natural number such that the sum of the numbers is 10 and the sums of the numbers placed diagonally are equal is
  A)
  4                      done clear
  B)
  8 done clear
  C)
  24                    done clear
  D)
  6 done clear
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• question_answer6)
  How many numbers can be made with the digits 3, 4, 5, 6, 7, 8 lying between 3000 and 4000, which are divisible by 5 while repetition of any digit not allowed in any number?
  A)
  60                     done clear
  B)
  12 done clear
  C)
  120                  done clear
  D)
  24 done clear
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• question_answer7)
  The sum of all the numbers of four different digits that can be made by using the digits 0, 1, 2, and 3 is
  A)
  26664   done clear
  B)
  39996 done clear
  C)
  38664  done clear
  D)
  none of these done clear
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• question_answer8)
  A class contains three girls and four boys. Every Saturday, five go on a picnic (a different group of student is sent every week). During the picnic, eac girl in the group is given a doll by the accompanying teacher. If all possible groups of five have gone for picnic once, the total number of dolls that the girls have got is
  A)
  21                     done clear
  B)
  45 done clear
  C)
  27                    done clear
  D)
  24 done clear
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• question_answer9)
  Number of ways in which a lawn-tennis mixed double be made from seven married couples if no husband and wife play in the same set is
  A)
  240                   done clear
  B)
  420 done clear
  C)
  720                  done clear
  D)
  none of these done clear
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• question_answer10)
  In how many ways can a team of 11 players be formed out of 25 players, if 6 out of them are always to be included and 5 always to be excluded
  A)
  2020     done clear
  B)
  2002 done clear
  C)
  2008                done clear
  D)
  8002 done clear
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• question_answer11)
  A candidate is required to answer 6 out of 10 questions, which are divided into two groups, each containing 5 questions, he is not permitted to attempt more than 4 questions from either group. The number of different ways in which the candidate can choose 6 questions is
  A)
  50                     done clear
  B)
  150 done clear
  C)
  200      done clear
  D)
  250 done clear
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• question_answer12)
  A person predicts the outcome of 20 cricket matches of his home team. Each match can result in either a win, loss, or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct is equal to
  A)
  \[^{20}{{C}_{10}}\times {{2}^{10}}\]           done clear
  B)
  \[^{20}{{C}_{10}}\times {{30}^{20}}\] done clear
  C)
  \[^{20}{{C}_{10}}\times {{30}^{10}}\]         done clear
  D)
  \[^{20}{{C}_{10}}\times {{2}^{20}}\] done clear
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• question_answer13)
  The number of triangles that can be formed with 10 points as vertices, n of them being collinear, is 110. Then n is
  A)
  3                      done clear
  B)
  4 done clear
  C)
  5         done clear
  D)
  6 done clear
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• question_answer14)
  The number of ways of choosing a committee of two women and three men from women and six men. If Mr. A refuses to serve on the committee if Mr. B is a member and Mr. B can only serve, if Miss C is the member of the committee is
  A)
  60                     done clear
  B)
  84 done clear
  C)
  124      done clear
  D)
  none of these done clear
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• question_answer15)
  The number of ways in which we can get a score of 11 by throwing three dice is
  A)
  18                     done clear
  B)
  27 done clear
  C)
  45                    done clear
  D)
  56 done clear
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• question_answer16)
  The number of ways to give 16 different things to three persons A,B,C so that B gets one more than A and C gets two more than B is
  A)
  \[\frac{16!}{4!5!7!}\]     done clear
  B)
  \[4!5!7!\] done clear
  C)
  \[\frac{16!}{3!5!8!}\]     done clear
  D)
  none of these done clear
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• question_answer17)
  The maximum number of points of intersection of five lines and four circles is
  A)
  60                     done clear
  B)
  72 done clear
  C)
  62                    done clear
  D)
  none of these done clear
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• question_answer18)
  Number of ways in which Rs. 18 can be distributed amongst four persons such that nobody receives less than Rs. 3 is
  A)
  \[{{4}^{2}}\]              done clear
  B)
  \[{{2}^{4}}\] done clear
  C)
  4!                    done clear
  D)
  none of these done clear
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• question_answer19)
  A man has three friends. The number of ways he can invite one friend every day for dinner on six successive nights so that no friend is invited more than three times is
  A)
  640       done clear
  B)
  320 done clear
  C)
  420                  done clear
  D)
  510 done clear
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• question_answer20)
  There are four letters and four directed envelopers. The number of ways in which all the letters can be put I the wrong envelope is
  A)
  8                      done clear
  B)
  9 done clear
  C)
  16                    done clear
  D)
  none of these done clear
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• question_answer21)
  Messages are conveyed by arranging four white, one blue, and three red flags on a pole. Flags of the same colures are alike. If a message is transmitted by the order in which the colours are arranged, the total number of messages that can be transmitted if exactly six flags are used is _______.
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• question_answer22)
  Five - digit number divisible by 3 are formed using 0, 1, 2, 3, 4, 5 without repetition. The total number of such numbers is______.
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• question_answer23)
  The total number of numbers greater then 1000 but less than 4000 formed using the digit 0, 1, 2, 3 and 4 (repetition allowed) is_____.
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• question_answer24)
  The sum of integers from 1 to 100 that are divisible by 2 or 5 is_____.
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• question_answer25)
  The total number of four-digit old numbers that can be formed using 0, 1, 2, 3, 5, and 7 (repetition allowed) is_____.
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