JEE Main & Advanced Mathematics Permutations and Combinations Question Bank

done Critical Thinking Questions Total Questions - 40

• question_answer1)
  The value of \[{{2}^{n}}\,\{1.3.5.....(2n-3)\,(2n-1)\}\] is
  A)
  \[\frac{(2n)\,!}{n\,!}\] done clear
  B)
  \[\frac{(2n)\,!}{{{2}^{n}}}\] done clear
  C)
  \[{{2}^{n-i}}\] done clear
  D)
  None of these done clear
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• question_answer2)
  A question paper is divided into two parts A and B and each part contains 5 questions. The number of ways in which a candidate can answer 6 questions selecting at least two questions from each part is [Roorkee 1980]
  A)
  80 done clear
  B)
  100 done clear
  C)
  200 done clear
  D)
  None of these done clear
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• question_answer3)
  How many numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is allowed)
  A)
  1024 done clear
  B)
  810 done clear
  C)
  2346 done clear
  D)
  None of these done clear
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• question_answer4)
  The number of ways in which the letters of the word TRIANGLE can be arranged such that two vowels do not occur together is
  A)
  1200 done clear
  B)
  2400 done clear
  C)
  14400 done clear
  D)
  None of these done clear
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• question_answer5)
  There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls, one in each box, could be placed such that a ball does not go to box of its own colour is [IIT 1992]
  A)
  8 done clear
  B)
  7 done clear
  C)
  9 done clear
  D)
  None of these done clear
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• question_answer6)
  If  \[^{56}{{P}_{r+6}}{{:}^{54}}{{P}_{r+3}}=30800:1\], then \[r=\] [Roorkee 1983; Kurukshetra CEE 1998]
  A)
  31 done clear
  B)
  41 done clear
  C)
  51 done clear
  D)
  None of these done clear
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• question_answer7)
  Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is                 [IIT 1980; MNR 1998, 99; DCE 2001]
  A)
  69760 done clear
  B)
  30240 done clear
  C)
  99748 done clear
  D)
  None of these done clear
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• question_answer8)
  The number of ways of dividing 52 cards amongst four players so that three players have 17 cards each and the fourth player just one card, is [IIT 1979]
  A)
  \[\frac{52\ !}{{{(17\ !)}^{3}}}\] done clear
  B)
  \[52\ !\] done clear
  C)
  \[\frac{52\ !}{17\ !}\] done clear
  D)
  None of these done clear
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• question_answer9)
  The number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together is [MP PET 1993]
  A)
  360 done clear
  B)
  900 done clear
  C)
  1260 done clear
  D)
  1620 done clear
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• question_answer10)
  A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the  draw [IIT 1986; DCE 1994]
  A)
  64 done clear
  B)
  45 done clear
  C)
  46 done clear
  D)
  None of these done clear
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• question_answer11)
  \[m\] men and n women are to be seated in a row so that no two women sit together. If \[m>n\], then the number of ways in which they can be seated is [IIT 1983]
  A)
  \[\frac{m\ !\ (m+1)\ !}{(m-n+1)\ !}\] done clear
  B)
  \[\frac{m\ !\ (m-1)\ !}{(m-n+1)\ !}\] done clear
  C)
  \[\frac{(m-1)\ !\ (m+1)\ !}{(m-n+1)\ !}\] done clear
  D)
  None of these done clear
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• question_answer12)
  A five digit number divisible by 3 has to formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total  number of ways in which this can be done is [IIT 1989; AIEEE 2002]
  A)
  216 done clear
  B)
  240 done clear
  C)
  600 done clear
  D)
  3125 done clear
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• question_answer13)
  In a certain test there are \[n\] questions. In the test \[{{2}^{n-i}}\] students gave wrong answers to at least \[i\] questions, where \[i=1,\ 2,\ ......n\]. If the total number of wrong answers given is 2047, then \[n\] is equal to
  A)
  10 done clear
  B)
  11 done clear
  C)
  12 done clear
  D)
  13 done clear
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• question_answer14)
  The number of times the digit 3 will be written when listing the integers from 1 to 1000 is
  A)
  269 done clear
  B)
  300 done clear
  C)
  271 done clear
  D)
  302 done clear
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• question_answer15)
  Ten persons, amongst whom are A, B and C to speak at a function. The number of ways in which it can be done if A wants to speak before B and B wants to speak before C is
  A)
  \[\frac{10\ !}{6}\] done clear
  B)
  \[3\ !\ 7\ !\] done clear
  C)
  \[^{10}{{P}_{3}}\ .\ 7\ !\] done clear
  D)
  None of these done clear
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• question_answer16)
  The number of ways in which an examiner can assign 30 marks to 8 questions, awarding not less than 2 marks to any question is
  A)
  \[^{21}{{C}_{7}}\] done clear
  B)
  \[^{30}{{C}_{16}}\] done clear
  C)
  \[^{21}{{C}_{16}}\] done clear
  D)
  None of these done clear
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• question_answer17)
  How many words can be made out from the letters of the word INDEPENDENCE, in which vowels always come together [Roorkee 1989]
  A)
  16800 done clear
  B)
  16630 done clear
  C)
  1663200 done clear
  D)
  None of these done clear
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• question_answer18)
  Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty [IIT 1981]
  A)
  50 done clear
  B)
  100 done clear
  C)
  150 done clear
  D)
  200 done clear
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• question_answer19)
  In how many ways can a committee be formed of 5 members from 6 men and 4 women if the committee has at least one woman [RPET 1987; IIT 1968; Pb. CET 2003]
  A)
  186 done clear
  B)
  246 done clear
  C)
  252 done clear
  D)
  None of these done clear
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• question_answer20)
  How many words can be made from the letters of the word BHARAT in which B and H never come together [IIT 1977]
  A)
  360 done clear
  B)
  300 done clear
  C)
  240 done clear
  D)
  120 done clear
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• question_answer21)
  There are 10 persons named \[A,\ B,.......J\]. We have the capacity to accommodate only 5. In how many ways can we arrange them in a line if \[A\] is must and \[G\] and \[H\] must not be included in the team of 5
  A)
  \[^{8}{{P}_{5}}\] done clear
  B)
  \[^{7}{{P}_{5}}\] done clear
  C)
  \[^{7}{{C}_{3}}(4\ !)\] done clear
  D)
  \[^{7}{{C}_{3}}(5\ !)\] done clear
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• question_answer22)
  The number of times the digit 5 will be written when listing the integers from 1 to 1000 is
  A)
  271 done clear
  B)
  272 done clear
  C)
  300 done clear
  D)
  None of these done clear
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• question_answer23)
  The exponent of 3 in \[100\ !\] is
  A)
  33 done clear
  B)
  44 done clear
  C)
  48 done clear
  D)
  52 done clear
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• question_answer24)
  The total number of different combinations of one or more letters which can be made from the letters of the word 'MISSISSIPPI' is
  A)
  150 done clear
  B)
  148 done clear
  C)
  149 done clear
  D)
  None of these done clear
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• question_answer25)
  A person goes in for an examination in which there are four papers with a maximum of \[m\] marks from each paper. The number of ways in which one can get \[2m\] marks is
  A)
  \[^{2m+3}{{C}_{3}}\] done clear
  B)
  \[\frac{1}{3}(m+1)(2{{m}^{2}}+4m+1)\] done clear
  C)
  \[\frac{1}{3}(m+1)(2{{m}^{2}}+4m+3)\] done clear
  D)
  None of these done clear
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• question_answer26)
  There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants is
  A)
  6 done clear
  B)
  11 done clear
  C)
  13 done clear
  D)
  None of these done clear
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• question_answer27)
  A father with 8 children takes them 3 at a time  to the Zoological gardens, as often as he can without taking the same 3 children together more than once. The number of times each child will go to the garden is
  A)
  56 done clear
  B)
  21 done clear
  C)
  112 done clear
  D)
  None of these done clear
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• question_answer28)
  A library has \[a\] copies of one book, \[b\] copies of each of two books, \[c\] copies of each of three books and single copies of \[d\] books. The total number of ways in which these books can be distributed is
  A)
  \[\frac{(a+b+c+d)\ !}{a\ !\ b\ !\ c\ !}\] done clear
  B)
  \[\frac{(a+2b+3c+d)\ !}{a\ !\ {{(b\ !)}^{2}}{{(c\ !)}^{3}}}\] done clear
  C)
  \[\frac{(a+2b+3c+d)\ !}{a\ !\ b\ !\ c\ !}\] done clear
  D)
  None of these done clear
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• question_answer29)
  A car will hold 2 in the front seat and 1 in the rear seat. If among 6 persons 2 can drive, then the number of ways in which the car can be filled is
  A)
  10 done clear
  B)
  20 done clear
  C)
  30 done clear
  D)
  None of these done clear
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• question_answer30)
  There are \[(n+1)\] white and \[(n+1)\] black balls each set numbered 1 to \[n+1\]. The number of ways in which the balls can be arranged in a row so that the adjacent balls are of different colours is [EAMCET 1991]
  A)
  \[(2n+2)\ !\] done clear
  B)
  \[(2n+2)\ !\ \times 2\] done clear
  C)
  \[(n+1)\ !\ \times 2\] done clear
  D)
  \[2{{\{(n+1)\ !\}}^{2}}\] done clear
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• question_answer31)
  12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is [EAMCET 1994]
  A)
  \[9(10\ !)\] done clear
  B)
  \[2(10\ !)\] done clear
  C)
  \[45(8\ !)\] done clear
  D)
  \[10\ !\] done clear
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• question_answer32)
  How many numbers between 5000 and 10,000 can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 each digit appearing not more than once in each number [Karnataka CET 1993]
  A)
  \[5{{\times }^{8}}{{P}_{3}}\] done clear
  B)
  \[5{{\times }^{8}}{{C}_{3}}\] done clear
  C)
  \[5\ !\ {{\times }^{8}}{{P}_{3}}\] done clear
  D)
  \[5\ !\ {{\times }^{8}}{{C}_{3}}\] done clear
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• question_answer33)
  If \[x,\ y\] and \[r\] are positive integers, then \[^{x}{{C}_{r}}{{+}^{x}}{{C}_{r-1}}^{y}{{C}_{1}}{{+}^{x}}{{C}_{r-2}}^{y}{{C}_{2}}+.......{{+}^{y}}{{C}_{r}}=\] [Karnataka CET 1993; RPET 2001]
  A)
  \[\frac{x\ !\ y\ !}{r\ !}\] done clear
  B)
  \[\frac{(x+y)\ !}{r\ !}\] done clear
  C)
  \[^{x+y}{{C}_{r}}\] done clear
  D)
  \[^{xy}{{C}_{r}}\] done clear
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• question_answer34)
  The number of ways in which an arrangement of 4 letters of the word 'PROPORTION' can be made is
  A)
  700 done clear
  B)
  750 done clear
  C)
  758 done clear
  D)
  800 done clear
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• question_answer35)
  The number of different words that can be formed out of the letters of the word 'MORADABAD' taken four at a time is
  A)
  500 done clear
  B)
  600 done clear
  C)
  620 done clear
  D)
  626 done clear
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• question_answer36)
  There are three girls in a class of 10 students. The number of different ways in which they can be seated in a row such that no two of the three girls are together is
  A)
  \[7\ !\ {{\times }^{6}}{{P}_{3}}\] done clear
  B)
  \[7\ !\ {{\times }^{8}}{{P}_{3}}\] done clear
  C)
  \[7\ !\ \times 3\ !\] done clear
  D)
  \[\frac{10\ !}{3\ !\ 7\ !}\] done clear
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• question_answer37)
  For \[2\le r\le n,\left( \begin{matrix}    n  \\    r  \\ \end{matrix} \right)+2\,\left( \begin{align}   & \,\,n \\  & r-1 \\ \end{align} \right)\]\[+\left( \begin{matrix}    n  \\    r-2  \\ \end{matrix} \right)\] is equal to    [IIT Screening 2000; Pb. CET 2000]
  A)
  \[\left( \begin{matrix}    n+1  \\    r-1  \\ \end{matrix} \right)\] done clear
  B)
  \[2\,\left( \begin{matrix}    n+1  \\    r+1  \\ \end{matrix} \right)\] done clear
  C)
  \[2\,\left( \begin{matrix}    n+2  \\    r  \\ \end{matrix} \right)\] done clear
  D)
  \[\left( \begin{matrix}    n+2  \\    r  \\ \end{matrix} \right)\] done clear
  View Solution play_arrow

• question_answer38)
  The number of positive integral solutions of \[a\,b\,c=30\]is [UPSEAT 2001]
  A)
  30 done clear
  B)
  27 done clear
  C)
  8 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer39)
  How many different nine-digit numbers can be formed from the digits of the number 223355888 by rearrangement of the digits so that the odd digits occupy even places  [IIT Screening 2000; Karnataka CET 2002]
  A)
  16 done clear
  B)
  36 done clear
  C)
  60 done clear
  D)
  180 done clear
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• question_answer40)
  A dictionary is printed consisting of 7 lettered words only that can be made with a letter of the word CRICKET. If the words are printed at the alphabetical order, as in an ordinary dictionary, then the number of word before the word CRICKET is [Orissa JEE 2003]
  A)
  530 done clear
  B)
  480 done clear
  C)
  531 done clear
  D)
  481 done clear
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