JEE Main & Advanced Mathematics Permutations and Combinations Question Bank

done Self Evaluation Test - Permutations and Combinatioins Total Questions - 70

• question_answer1)
  Three boys and three girls are to be seated around a table, in a circle. Among them, the boy X does not want any girl neighbour and the girls Y does not want any boy neighbour. The number of such arrangements possible is
  A)
  4 done clear
  B)
  6 done clear
  C)
  8 done clear
  D)
  None of these   done clear
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• question_answer2)
  There are three men and seven women taking a dance class. Number of different ways in which each man is paired with a woman partner, and the four remaining women are paired into two pairs each of two is
  A)
  105 done clear
  B)
  315 done clear
  C)
  630 done clear
  D)
  450 done clear
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• question_answer3)
  Seven people leave their bags outside temple and while returning after worshiping the deity, picked one bag each at random. In how many ways at least one and at most three of them get their correct bags?
  A)
  \[^{7}{{C}_{3}}.9{{+}^{7}}{{C}_{5}}.44{{+}^{7}}{{C}_{1}}.265\] done clear
  B)
  \[^{7}{{C}_{6}}.265{{+}^{7}}{{C}_{5}}.9{{+}^{7}}{{C}_{7}}.44\] done clear
  C)
  \[^{7}{{C}_{5}}.9{{+}^{7}}{{C}_{2}}.44{{+}^{7}}{{C}_{1}}.265\] done clear
  D)
  None of these done clear
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• question_answer4)
  Four couples (husband and wife) decide to form a committee of four members. Find the number of different committees that can be formed in which no couple finds a place.
  A)
  12 done clear
  B)
  14 done clear
  C)
  16 done clear
  D)
  24 done clear
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• question_answer5)
  The sides AB, BC, CA, of a triangle ABC have 3, 4 and 5 interior points respectively on them. The total number of triangles that can be constructed by using these points as vertices is
  A)
  220 done clear
  B)
  204 done clear
  C)
  205 done clear
  D)
  195 done clear
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• question_answer6)
  A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is:
  A)
  40 done clear
  B)
  41 done clear
  C)
  16 done clear
  D)
  32 done clear
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• question_answer7)
  If all permutations of the letters of the word AGAIN are arranged as in dictionary, then fiftieth word is
  A)
  NAAGI done clear
  B)
  NAGAI done clear
  C)
  NAAIG done clear
  D)
  NAIAG done clear
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• question_answer8)
  How many numbers with no more than three digits can be formed using only the digits 1 through 7 with no digit used more than once in a given number?
  A)
  259 done clear
  B)
  249 done clear
  C)
  257 done clear
  D)
  252 done clear
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• question_answer9)
  The value of \[{{1}^{2}}.{{C}_{1}}+{{3}^{2}}.{{C}_{3}}+{{5}^{2}}.{{C}_{5}}+...\] is:
  A)
  \[n{{(n-1)}^{n-2+n{{.2}^{n-1}}}}\] done clear
  B)
  \[n{{(n-1)}^{n-2}}\] done clear
  C)
  \[n{{(n-1)}^{n-3}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer10)
  In how many ways vertices of a square can be coloured with 4 distinct colour if rotations are considered to be equivalent, but reflections are distinct?
  A)
  65 done clear
  B)
  70 done clear
  C)
  71 done clear
  D)
  None of these done clear
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• question_answer11)
  The total number of 5 digit numbers of different digits in which the digit in the middle is the largest, is
  A)
  \[\sum\limits_{n=4}^{9}{^{n}{{P}_{4}}}\] done clear
  B)
  \[\sum\limits_{n=4}^{9}{^{n}{{P}_{4}}}-\frac{1}{3!}\sum\limits_{n=3}^{9}{^{n}{{P}_{3}}}\] done clear
  C)
  \[30(3!)\] done clear
  D)
  None of these done clear
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• question_answer12)
  If\[n={{2}^{p-1}}({{2}^{p}}-1)\], where \[{{2}^{p}}-1\] is a prime, then the sum of the divisors of n is equal to
  A)
  n done clear
  B)
  2n done clear
  C)
  pn done clear
  D)
  \[{{p}^{n}}\] done clear
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• question_answer13)
  The value of ?n? for which \[^{n-1}{{C}_{4}}{{-}^{n-1}}{{C}_{3}}-\frac{5}{4}{{.}^{n-1}}{{P}_{2}}<0,\] Where \[n\in N\]
  A)
  \[\{5,6,7,8,9,10\}\] done clear
  B)
  \[\{1,2,3,4,5,6,7,8,9,10\}\] done clear
  C)
  \[\{1,4,5,6,7,8,9,10\}\] done clear
  D)
  \[(-\infty ,2)\cup (3,11)\] done clear
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• question_answer14)
  Let P be a prime number such that \[p\ge 11.\] Let \[n=p!+1.\] The number of primes in the list \[n+1,\] \[n+2,n+3,...n+P-1,\] is
  A)
  \[p-1\] done clear
  B)
  2 done clear
  C)
  1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer15)
  A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
  A)
  346 done clear
  B)
  140 done clear
  C)
  196 done clear
  D)
  280 done clear
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• question_answer16)
  If \[S=(1)(1!)+(2)(2!)+(3)(3!)+...+n(n!),\] then
  A)
  \[\frac{S+1}{n!}\in \]integer done clear
  B)
  \[\frac{S+1}{n!}\notin \] Integer done clear
  C)
  \[\frac{S+1}{n!}\] cannot be discussed done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer17)
  Find the number of integral solution of the equation \[x+y+z=20\] and \[x>-1,y>-2\] and \[z>-3.\]
  A)
  \[^{25}{{C}_{23}}\] done clear
  B)
  \[^{17}{{C}_{2}}\] done clear
  C)
  \[^{23}{{C}_{2}}\]      done clear
  D)
  None of these done clear
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• question_answer18)
  There are 10 bags \[{{B}_{1}},{{B}_{2}},{{B}_{3}},...,{{B}_{10}},\]which contain 21, 22? 30 different articles respectively. The total number of ways to bring out 10 articles from a bag is
  A)
  \[^{31}{{C}_{20}}{{-}^{21}}{{C}_{10}}\]    done clear
  B)
  \[^{31}{{C}_{21}}\] done clear
  C)
  \[^{31}{{C}_{20}}\] done clear
  D)
  None of these done clear
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• question_answer19)
  If 16 identical pencils are distributed among 4 children such that each gets at least 3 pencils. The number of ways of distributing the pencils is
  A)
  15 done clear
  B)
  25 done clear
  C)
  35 done clear
  D)
  40 done clear
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• question_answer20)
  In how many ways a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 are 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_answer21)
  The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
  A)
  \[^{8}{{C}_{3}}\] done clear
  B)
  21 done clear
  C)
  \[{{3}^{8}}\] done clear
  D)
  5 done clear
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• question_answer22)
  The number of six digit numbers that can be formed from the digits \[1,2,3,4,5,6\] and 7 so that digits do not repeat and the terminal digits are even, is
  A)
  144 done clear
  B)
  72 done clear
  C)
  288 done clear
  D)
  720 done clear
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• question_answer23)
  There are 10 points in a plane, no three are collinear, except 4 which are collinear. All points are joined. Let L be the number of different straight lines and T be the number of different triangles, then
  A)
  \[T=120\] done clear
  B)
  \[L=40\] done clear
  C)
  \[T=3L-5\] done clear
  D)
  None of these done clear
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• question_answer24)
  In a 12 -storey house ten people enter a lift cabin. It is known that they will left in groups of 2,3 and 5 people at different storeys. The number of ways they can do so if the left does not stop to the second storey is
  A)
  78 done clear
  B)
  112 done clear
  C)
  720 done clear
  D)
  132   done clear
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• question_answer25)
  A person writes letters to six friends and be the number of ways so that at least two of the number of ways so that all the letters are in wrong envelopes. Then \[\operatorname{x} - y =\]
  A)
  719 done clear
  B)
  265 done clear
  C)
  454 done clear
  D)
  None done clear
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• question_answer26)
  A person invites a party of 10 friends at dinner and place them so that 4 are on one round table and 6 on the other round table. The number of ways in which he can arrange the guests is
  A)
  \[\frac{(10)!}{6!}\] done clear
  B)
  \[\frac{(10)!}{24}\] done clear
  C)
  \[\frac{(9)!}{24}\] done clear
  D)
  None of these done clear
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• question_answer27)
  Ten different letters of an alphabet are given, words with five letters are formed form these given letters. Then the number of words which have at least one letter repeated is
  A)
  69760 done clear
  B)
  30240 done clear
  C)
  99784 done clear
  D)
  None of these done clear
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• question_answer28)
  A boat is to be manned by eight men of whom 2 can only row on bow side and 3 can only row on stroke side, the number of ways in which the crew can be arranged is
  A)
  4360 done clear
  B)
  5760 done clear
  C)
  5930     done clear
  D)
  None of these done clear
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• question_answer29)
  The number of distinct rational numbers x such that \[0<x<1\] and \[x=\frac{p}{q},\] where \[p,q\in \{1,2,3,4,5,6\},\] is
  A)
  15 done clear
  B)
  13 done clear
  C)
  12 done clear
  D)
  11 done clear
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• question_answer30)
  In a small village, there are 87 families, of which 52 families have at most 2 children. In a rural development programme 20 families are to be chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
  A)
  \[^{52}{{C}_{18}}^{35}{{C}_{2}}\] done clear
  B)
  \[^{52}{{C}_{18}}{{\times }^{35}}{{C}_{2}}{{+}^{52}}{{C}_{19}}{{\times }^{35}}{{C}_{1}}{{+}^{52}}{{C}_{20}}\] done clear
  C)
  \[^{52}{{C}_{18}}{{+}^{35}}{{C}_{2}}{{+}^{52}}{{C}_{19}}\] done clear
  D)
  \[^{52}{{C}_{18}}{{\times }^{35}}{{C}_{2}}{{+}^{35}}{{C}_{1}}{{\times }^{52}}{{C}_{19}}\] done clear
  View Solution play_arrow

• question_answer31)
  The straight lines \[{{\ell }_{1}},{{\ell }_{2}},{{\ell }_{3}}\] and parallel and lie in the same plane. A total number of m points are taken on \[{{\ell }_{1}}\], n points on \[{{\ell }_{2}}\]. k points on \[{{\ell }_{3}}\]. The maximum number of triangles formed with vertices at these points are:
  A)
  \[^{m+n+k}{{C}_{3}}\] done clear
  B)
  \[^{m+n+k}{{C}_{3}}{{-}^{m}}{{C}_{3}}{{-}^{n}}{{C}_{3}}{{-}^{k}}{{C}_{3}}\] done clear
  C)
  \[^{m}{{C}_{3}}{{+}^{m}}{{C}_{3}}{{+}^{k}}{{C}_{3}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer32)
  All the words that can be formed using alphabets A, H, L, U and R are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is
  A)
  71 done clear
  B)
  72 done clear
  C)
  73 done clear
  D)
  74 done clear
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• question_answer33)
  'n' is selected form the set \[\{1,2,3...,100\}\]and the number \[{{2}^{n}}+{{3}^{n}}+{{5}^{n}}\] is formed. Total number of ways of selecting 'n' so that the formed number is divisible by 4, is equal to
  A)
  50 done clear
  B)
  49 done clear
  C)
  48 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer34)
  Let \[1\le m<n\le p.\]The number of subsets of the set \[A=\{1,2,3,...p\}\] having m, n as the least and the greatest elements respectively, is
  A)
  \[{{2}^{n-m-1}}-1\] done clear
  B)
  \[{{2}^{n-m-1}}\] done clear
  C)
  \[{{2}^{n-m}}\]           done clear
  D)
  \[{{2}^{p-n+m-1}}\] done clear
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• question_answer35)
  The number of ways in which a mixed doubles game in tennis can be arranged form 5 married couples, if no husband and wife play in the same game, is
  A)
  46 done clear
  B)
  54 done clear
  C)
  60 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer36)
  The total number of 3-digit numbers, the sum of whose digits is even, is equal to
  A)
  450 done clear
  B)
  350 done clear
  C)
  250 done clear
  D)
  325 done clear
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• question_answer37)
  There are 18 points in a plane such that no three of them are in the same line except five points which are collinear. The number of triangles formed by these points is:
  A)
  816 done clear
  B)
  806 done clear
  C)
  805 done clear
  D)
  813 done clear
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• question_answer38)
  Find the number of non-negative solutions of the systems of equations: \[a+b=10,a+b+c+d=21,a+b+c+d+e+f=33,\]\[a+b+c+d+e+f+g+h=46\], and so on till \[a+b+c+d+....+x+y+z=208.\]
  A)
  \[^{22}{{P}_{10}}\] done clear
  B)
  \[^{22}{{P}_{11}}\] done clear
  C)
  \[^{22}{{P}_{13}}\] done clear
  D)
  None of these   done clear
  View Solution play_arrow

• question_answer39)
  Two straight line intersect at a point O. Points \[{{A}_{1}},{{A}_{2}},...{{A}_{n}}\] are taken on one line and pints \[{{B}_{1}},{{B}_{2}},...,{{B}_{n}}\]on the other. If the point O is not to be used, the number of triangles that can be drawn using these points as vertices, is
  A)
  \[n(n-1)\] done clear
  B)
  \[n{{(n-1)}^{2}}\] done clear
  C)
  \[{{n}^{2}}(n-1)\] done clear
  D)
  \[{{n}^{2}}{{(n-1)}^{2}}\] done clear
  View Solution play_arrow

• question_answer40)
  5 - Digit numbers are to be formed using 2, 3, 5, 7, 9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000, then p:q is:
  A)
  \[6:5\] done clear
  B)
  \[3:2\] done clear
  C)
  \[4:3\] done clear
  D)
  \[5:3\] done clear
  View Solution play_arrow

• question_answer41)
  Number of ways in which 20 different pearls of two colours can be set alternately on a necklace, there being 10 pearls of each colour.
  A)
  \[6\times {{(9!)}^{2}}\] done clear
  B)
  12! done clear
  C)
  \[4\times {{(8!)}^{2}}\] done clear
  D)
  \[5\times {{(9!)}^{2}}\] done clear
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• question_answer42)
  If 12 persons are seated in a row, the number of ways of selecting 3 persons from them, so that no two of them are seated next to each other is
  A)
  85 done clear
  B)
  100 done clear
  C)
  120 done clear
  D)
  240 done clear
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• question_answer43)
  The number of permutations of the letters of the word HINDUSTAN such that neither the pattern ?HIN? nor ?DUS? nor ?TAN? appears, are
  A)
  166674 done clear
  B)
  169194 done clear
  C)
  166680 done clear
  D)
  181434 done clear
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• question_answer44)
  A shop keeper sells three varieties of perfumes and he has a large number of bottles of the same size of each variety in this stock. There are 5 places in a row in his show case. The number of different ways of displaying the three varieties of perfumes in the show case is
  A)
  6 done clear
  B)
  50 done clear
  C)
  150 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer45)
  Consider n points in a plane no three of which are collinear and the ratio of number of hexagon and octagon that can be formed from these n points is 4:13 then find the value of n.
  A)
  14 done clear
  B)
  20 done clear
  C)
  28 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer46)
  A seven digit number divisible by 9 is to be formed by using 7 out of number\[\{1,2,3,4,5,6,7,8,9\}\]. The number of ways in which this can be done is
  A)
  \[7!\] done clear
  B)
  \[2\times 7!\] done clear
  C)
  \[3\times 7!\] done clear
  D)
  \[4\times 7!\] done clear
  View Solution play_arrow

• question_answer47)
  Total number of words that can be formed using all letters of the word FAILIRE which neither begin with F nor end with E is equal to
  A)
  3720 done clear
  B)
  5040 done clear
  C)
  3600     done clear
  D)
  3480 done clear
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• question_answer48)
  The expression \[^{n}{{C}_{r}}+{{4.}^{n}}{{C}_{r-1}}+{{6.}^{n}}{{C}_{r-2}}+{{4.}^{n}}{{C}_{r-3}}\]\[{{+}^{n}}{{C}_{r-4}}\] is equal to
  A)
  \[^{n+4}{{C}_{r}}\] done clear
  B)
  \[{{2.}^{n+4}}{{C}_{r-1}}\] done clear
  C)
  \[{{4.}^{n}}{{C}_{r}}\] done clear
  D)
  \[{{11.}^{n}}{{C}_{r}}\] done clear
  View Solution play_arrow

• question_answer49)
  A teaparty is arranged for 16 people along two sides of a large table with 8 chairs on each side. Four men want to sit on one particular side and two on the other side. The number of ways in which they can be seated is
  A)
  \[\frac{6!8!10!}{4!6!}\] done clear
  B)
  \[\frac{8!8!10!}{4!6!}\] done clear
  C)
  \[\frac{8!8!6!}{6!4!}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer50)
  The greatest common divisor of \[^{20}{{C}_{1}}{{,}^{20}}{{C}_{3}},...{{,}^{20}}{{C}_{19}}\] is
  A)
  20 done clear
  B)
  4 done clear
  C)
  5 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer51)
  Six teachers and sic students have to sit round a circular table such that there is a teacher between any two students. The number of ways I which they can sit is
  A)
  \[6!\times 6!\] done clear
  B)
  \[5!\times 6!\] done clear
  C)
  \[5!\,\times 5!\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer52)
  Let \[E=(2n+1)(2n+3)(2n+5)...(4n-3)(4n-1);\] \[n>1\] then \[{{2}^{n}}E\] divisible by
  A)
  \[^{n}{{C}_{n/2}}\] done clear
  B)
  \[^{2n}{{C}_{n}}\] done clear
  C)
  \[^{3n}{{C}_{n}}\]      done clear
  D)
  \[^{4n}{{C}_{2n}}\] done clear
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• question_answer53)
  In a plane there are 37 straight lines of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no line passes through both points A and B, and no two are parallel. Then the number of intersection points the lines have is equal to
  A)
  535 done clear
  B)
  601 done clear
  C)
  728 done clear
  D)
  None of these   done clear
  View Solution play_arrow

• question_answer54)
  The number of different words which can be formed from the letters of the word LUCKNOW when the vowels always occupy even places in
  A)
  120 done clear
  B)
  720 done clear
  C)
  400 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer55)
  The least positive integral values of n which satisfies the inequality \[^{10}{{C}_{n-1}}>{{2.}^{10}}{{C}_{n}}\]
  A)
  7 done clear
  B)
  8 done clear
  C)
  9 done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer56)
  If a denotes the number of permutations of x+2 things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x -11 things taken all at a time such that \[a=182\,\,bc,\] then the value of x will be
  A)
  12 done clear
  B)
  10 done clear
  C)
  8 done clear
  D)
  6 done clear
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• question_answer57)
  If \[\frac{2}{9!}+\frac{2}{3!7!}+\frac{1}{5!5!}=\frac{{{2}^{a}}}{b!},\] where \[a,b\in N,\]then the ordered pair (a, b) is
  A)
  \[(9,10)\] done clear
  B)
  \[(10,9)\] done clear
  C)
  \[(7,10)\] done clear
  D)
  \[(10,7)\] done clear
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• question_answer58)
  The set \[S=\{1,2,3,...,12\}\] is to be partitioned into three sets, A, B, C of equal size. Thus\[A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\phi \]. The number of ways to partition S is
  A)
  \[\frac{12!}{{{(4!)}^{3}}}\] done clear
  B)
  \[\frac{12!}{{{(4!)}^{4}}}\] done clear
  C)
  \[\frac{12!}{3!{{(4!)}^{3}}}\] done clear
  D)
  \[\frac{12!}{3!{{(4!)}^{4}}}\] done clear
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• question_answer59)
  Ravish writes letters to his five friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes?
  A)
  109 done clear
  B)
  118 done clear
  C)
  119 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer60)
  \[f:\{1,2,3,4,5\}\to \{1,2,3,4,5\}\] that are onto and \[f(i)\ne i,\] is equal to
  A)
  9 done clear
  B)
  44 done clear
  C)
  16 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer61)
  Let \[{{T}_{n}}\] denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If \[{{T}_{n+1}}-{{T}_{n}}=21\], then n equals
  A)
  5 done clear
  B)
  7 done clear
  C)
  6 done clear
  D)
  4 done clear
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• question_answer62)
  How many different nine digit numbers can be formed form the number 223355888 by rearranging its digits so that the odd digits occupy even positions?
  A)
  16 done clear
  B)
  36 done clear
  C)
  60 done clear
  D)
  180 done clear
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• question_answer63)
  Let \[S=\sum\limits_{k=0}^{n-1}{^{k+2}{{P}_{2}},}\] then
  A)
  n divides 3S done clear
  B)
  n+1 divides 3S done clear
  C)
  n+2 divides 3S done clear
  D)
  All are correct done clear
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• question_answer64)
  How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?
  A)
  18 done clear
  B)
  28 done clear
  C)
  6 done clear
  D)
  27 done clear
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• question_answer65)
  How many different words can be formed by jumbling the letters in the word MISSISSIOOI in which no two S are adjacent?
  A)
  \[{{8.}^{6}}{{C}_{4}}{{.}^{7}}{{C}_{4}}\] done clear
  B)
  \[{{6.7.}^{8}}{{C}_{4}}\] done clear
  C)
  \[{{6.8.}^{7}}{{C}_{4}}.\] done clear
  D)
  \[{{7.}^{6}}{{C}_{4}}{{.}^{8}}{{C}_{4}}\] done clear
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• question_answer66)
  From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is:
  A)
  At least 500 but less than 750 done clear
  B)
  At least 750 but less than 1000 done clear
  C)
  At least 1000 done clear
  D)
  Less than 500 done clear
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• question_answer67)
  The sum of all the numbers of four different digits that can be made by using the digits 0, 1, 2 and 3.
  A)
  64322 done clear
  B)
  48522 done clear
  C)
  38664 done clear
  D)
  1000   done clear
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• question_answer68)
  The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is:
  A)
  \[^{30}{{C}_{7}}\] done clear
  B)
  \[^{21}{{C}_{8}}\] done clear
  C)
  \[^{21}{{C}_{7}}\]      done clear
  D)
  \[^{30}{{C}_{8}}\] done clear
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• question_answer69)
  Let \[A=\{x|x\] is prime number and\[x<30\}\]. The number of different rational numbers whose numerator and denominator belong to A is
  A)
  90 done clear
  B)
  180 done clear
  C)
  91 done clear
  D)
  100 done clear
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• question_answer70)
  If \[^{n}{{C}_{r-1}}{{+}^{n+1}}{{C}_{r-1}}{{+}^{n+2}}{{C}_{r-1}}+...{{+}^{2n}}{{C}_{r-1}}\] \[{{=}^{2n+1}}{{C}_{{{r}^{2}}-132}}{{-}^{n}}{{C}_{r}},\] Then the value of r and the minimum value of n are
  A)
  10 done clear
  B)
  11 done clear
  C)
  12 done clear
  D)
  13 done clear
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