JEE Main & Advanced Mathematics Permutations and Combinations Question Bank

done Definition of combinations, Conditional combinations, Division into groups, Derangements Total Questions - 85

• question_answer1)
  If \[n\] is even and the value of  \[^{n}{{C}_{r}}\] is maximum, then \[r=\]
  A)
  \[\frac{n}{2}\] done clear
  B)
  \[\frac{n+1}{2}\] done clear
  C)
  \[\frac{n-1}{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer2)
  A man has 7 friends. In how many ways he can invite one or more of them for a tea party
  A)
  128 done clear
  B)
  256 done clear
  C)
  127 done clear
  D)
  130 done clear
  View Solution play_arrow

• question_answer3)
  There are 12 volleyball players in all in a college, out of which a team of 9 players is to be formed. If the captain always remains the same, then in how many ways can the team be formed
  A)
  36 done clear
  B)
  108 done clear
  C)
  99 done clear
  D)
  165 done clear
  View Solution play_arrow

• question_answer4)
  In how many ways can a girl and a boy be selected from a group of 15 boys and 8 girls
  A)
   \[15\times 8\] done clear
  B)
  \[15+8\] done clear
  C)
  \[^{23}{{P}_{2}}\] done clear
  D)
  \[^{23}{{C}_{2}}\] done clear
  View Solution play_arrow

• question_answer5)
  If \[^{15}{{C}_{3r}}{{=}^{15}}{{C}_{r+3}}\], then the value of \[r\] is [IIT 1967; RPET 1991; MP PET 1998; Karnataka CET 1996]
  A)
  3 done clear
  B)
  4 done clear
  C)
  5 done clear
  D)
  8 done clear
  View Solution play_arrow

• question_answer6)
  \[^{47}{{C}_{4}}+\underset{r=1}{\overset{5}{\mathop{\sum }}}\,{}^{52-r}{{C}_{3}}=\] [IIT 1980; RPET 2002; UPSEAT 2000]
  A)
  \[^{47}{{C}_{6}}\] done clear
  B)
  \[^{52}{{C}_{5}}\] done clear
  C)
  \[^{15}{{C}_{15}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  \[^{n}{{C}_{r}}{{\div }^{n}}{{C}_{r-1}}=\] [MP PET 1984]
  A)
  \[\frac{n-r}{r}\] done clear
  B)
  \[\frac{n+r-1}{r}\] done clear
  C)
  \[\frac{n-r+1}{r}\] done clear
  D)
  \[\frac{n-r-1}{r}\] done clear
  View Solution play_arrow

• question_answer8)
  If  \[^{2n}{{C}_{3}}:{{\,}^{n}}{{C}_{2}}=44:3\],  then for which of the following  values of \[r\], the value of  \[^{n}{{C}_{r}}\] will be 15 [MP PET 1981]
  A)
  \[r=3\] done clear
  B)
  \[r=4\] done clear
  C)
  \[r=6\] done clear
  D)
  \[r=5\] done clear
  View Solution play_arrow

• question_answer9)
  If \[2\times {}^{n}{{C}_{5}}=9\,\,\times \,\,{}^{n-2}{{C}_{5}}\],  then the value of n will be
  A)
  7 done clear
  B)
  10 done clear
  C)
  9 done clear
  D)
  5 done clear
  View Solution play_arrow

• question_answer10)
  If  \[^{{{n}^{2}}-n}{{C}_{2}}{{=}^{{{n}^{2}}-n}}{{C}_{10}}\], then \[n=\]
  A)
  12 done clear
  B)
  4 only done clear
  C)
  \[-3\]only done clear
  D)
  4 or \[-3\] done clear
  View Solution play_arrow

• question_answer11)
  If  \[^{n}{{C}_{r-1}}=36,{{\ }^{n}}{{C}_{r}}=84\] and  \[^{n}{{C}_{r+1}}=126\], then the value of \[r\] is           [IIT 1979; Pb. CET 1993, 2003; DCE 1999, 2000; MP PET 2001]
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  \[^{n}{{C}_{r}}+{{2}^{n}}{{C}_{r-1}}{{+}^{n}}{{C}_{r-2}}=\]
  A)
  \[^{n+1}{{C}_{r}}\] done clear
  B)
  \[^{n+1}{{C}_{r+1}}\] done clear
  C)
  \[^{n+2}{{C}_{r}}\] done clear
  D)
  \[^{n+2}{{C}_{r+1}}\] done clear
  View Solution play_arrow

• question_answer13)
  In a conference of 8 persons, if each person shake hand with the other one only, then the total number of shake hands shall be [MP PET 1984]
  A)
  64 done clear
  B)
  56 done clear
  C)
  49 done clear
  D)
  28 done clear
  View Solution play_arrow

• question_answer14)
  \[^{n}{{C}_{r}}{{+}^{n}}{{C}_{r-1}}\] is equal to [MP PET 1984; Kerala (Engg.) 2002]
  A)
  \[^{n+1}{{C}_{r}}\] done clear
  B)
  \[^{n}{{C}_{r+1}}\] done clear
  C)
  \[^{n+1}{{C}_{r+1}}\] done clear
  D)
  \[^{n-1}{{C}_{r-1}}\] done clear
  View Solution play_arrow

• question_answer15)
  If \[^{8}{{C}_{r}}{{=}^{8}}{{C}_{r+2}}\], then the value of \[^{r}{{C}_{2}}\] is [MP PET 1984; RPET 1987]
  A)
  8 done clear
  B)
  3 done clear
  C)
  5 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer16)
  If \[^{20}{{C}_{n+2}}{{=}^{n}}{{C}_{16}}\], then the value of \[n\] is [MP PET 1984]
  A)
  7 done clear
  B)
  10 done clear
  C)
  13 done clear
  D)
  No value done clear
  View Solution play_arrow

• question_answer17)
  The value of \[^{15}{{C}_{3}}{{+}^{15}}{{C}_{13}}\] is [MP PET 1983]
  A)
  \[^{16}{{C}_{3}}\] done clear
  B)
  \[^{30}{{C}_{16}}\] done clear
  C)
  \[^{15}{{C}_{10}}\] done clear
  D)
  \[^{15}{{C}_{15}}\] done clear
  View Solution play_arrow

• question_answer18)
  Everybody in a room shakes hand with everybody else. The total number of hand shakes is 66. The total number of persons in the room is  [MNR 1991; Kurukshetra CEE 1998; Kerala (Engg.) 2001]
  A)
  11 done clear
  B)
  12 done clear
  C)
  13 done clear
  D)
  14 done clear
  View Solution play_arrow

• question_answer19)
  The solution set of \[^{10}{{C}_{x-1}}>2\ .{{\ }^{10}}{{C}_{x}}\] is
  A)
  {1, 2, 3} done clear
  B)
  {4, 5, 6} done clear
  C)
  {8,9, 10} done clear
  D)
  {9, 10, 11} done clear
  View Solution play_arrow

• question_answer20)
  \[\sum\limits_{r=0}^{m}{^{n+r}{{C}_{n}}=}\] [Pb. CET 2003]
  A)
  \[^{n+m+1}{{C}_{n+1}}\] done clear
  B)
  \[^{n+m+2}{{C}_{n}}\] done clear
  C)
  \[^{n+m+3}{{C}_{n-1}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer21)
  In a football championship, there were played 153 matches. Every team played one match with each other. The number of teams participating in the championship is   [WB JEE 1992; Kurukshetra CEE 1998]
  A)
  17 done clear
  B)
  18 done clear
  C)
  9 done clear
  D)
  13 done clear
  View Solution play_arrow

• question_answer22)
  In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answers correct, is [Pb. CET 1990; UPSEAT 2001]
  A)
  11 done clear
  B)
  12 done clear
  C)
  27 done clear
  D)
  63 done clear
  View Solution play_arrow

• question_answer23)
  If \[\alpha {{=}^{m}}{{C}_{2}}\], then \[^{\alpha }{{C}_{2}}\]is equal to
  A)
  \[^{m+1}{{C}_{4}}\] done clear
  B)
  \[^{m-1}{{C}_{4}}\] done clear
  C)
  \[3\,.{{\ }^{m+2}}{{C}_{4}}\] done clear
  D)
  \[3\ .{{\ }^{m+1}}{{C}_{4}}\] done clear
  View Solution play_arrow

• question_answer24)
  On the occasion of Deepawali festival each student of a class sends greeting cards to the others. If there are 20 students in the class, then the total number of greeting cards exchanged by the students is
  A)
  \[^{20}{{C}_{2}}\] done clear
  B)
  \[2\ .{{\ }^{20}}{{C}_{2}}\] done clear
  C)
  \[2\ .{{\ }^{20}}{{P}_{2}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer25)
  In a city no two persons have identical set of teeth and there is no person without a tooth. Also no person has more than 32 teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, then the maximum population of the city is
  A)
  \[{{2}^{32}}\] done clear
  B)
  \[{{(32)}^{2}}-1\] done clear
  C)
  \[{{2}^{32}}-1\] done clear
  D)
  \[{{2}^{32-1}}\] done clear
  View Solution play_arrow

• question_answer26)
  If \[^{2n}{{C}_{2}}{{:}^{n}}{{C}_{2}}=9:2\] and \[^{n}{{C}_{r}}=10\], then \[r=\]
  A)
  1 done clear
  B)
  2 done clear
  C)
  4 done clear
  D)
  5 done clear
  View Solution play_arrow

• question_answer27)
  If  \[^{10}{{C}_{r}}{{=}^{10}}{{C}_{r+2}}\], then  \[^{5}{{C}_{r}}\] equals [RPET 1996]
  A)
  120 done clear
  B)
  10 done clear
  C)
  360 done clear
  D)
  5 done clear
  View Solution play_arrow

• question_answer28)
  If \[^{n}{{C}_{r}}=84,{{\ }^{n}}{{C}_{r-1}}=36\] and \[^{n}{{C}_{r+1}}=126\], then \[n\] equals [RPET 1997; MP PET 2001]
  A)
  8 done clear
  B)
  9 done clear
  C)
  10 done clear
  D)
  5 done clear
  View Solution play_arrow

• question_answer29)
  If \[^{n}{{C}_{3}}+{{\,}^{n}}{{C}_{4}}>{{\,}^{n+1}}{{C}_{3}},\]then [RPET 1999]
  A)
  \[n>6\] done clear
  B)
  \[n>7\] done clear
  C)
  \[n<6\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer30)
  Value of r for which \[^{15}{{C}_{r+3}}={{\,}^{15}}{{C}_{2r-6}}\] is [Pb. CET 1999]
  A)
  2 done clear
  B)
  4 done clear
  C)
  6 done clear
  D)
  - 9 done clear
  View Solution play_arrow

• question_answer31)
  If \[^{n+1}{{C}_{3}}=2{{\,}^{n}}{{C}_{2}},\] then n = [MP PET 2000; Pb. CET 2002]
  A)
  3 done clear
  B)
  4 done clear
  C)
  5 done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer32)
  \[\left( \begin{matrix}    n  \\    n-r  \\ \end{matrix} \right)\,+\,\left( \begin{matrix}    n  \\    r+1  \\ \end{matrix} \right)\], whenever \[0\le r\le n-1\]is equal to [AMU 2000]
  A)
  \[\left( \begin{matrix}    n  \\    r-1  \\ \end{matrix} \right)\] done clear
  B)
  \[\left( \begin{matrix}    n  \\    r  \\ \end{matrix} \right)\] done clear
  C)
  \[\left( \begin{matrix}    n  \\    r+1  \\ \end{matrix} \right)\] done clear
  D)
  \[\left( \begin{matrix}    n+1  \\    r+1  \\ \end{matrix} \right)\] done clear
  View Solution play_arrow

• question_answer33)
  The least value of natural number n satisfying  \[C(n,\,5)+C(n,\,6)\,\,>C(n+1,\,5)\] is [EAMCET 2002]
  A)
  11 done clear
  B)
  10 done clear
  C)
  12 done clear
  D)
  13 done clear
  View Solution play_arrow

• question_answer34)
  There are 15 persons in a party and each person shake hand with another, then total number of hand shakes is [RPET 2002]
  A)
  \[^{15}{{P}_{2}}\] done clear
  B)
  \[^{15}{{C}_{2}}\] done clear
  C)
  \[15\,!\] done clear
  D)
  \[2\,(15\,!)\] done clear
  View Solution play_arrow

• question_answer35)
  If \[n\] and \[r\] are two positive integers such that \[n\ge r,\] then \[^{n}{{C}_{r-1}}\]\[+{{\,}^{n}}{{C}_{r}}=\]              [Kerala (Engg.) 2002]
  A)
  \[^{n}{{C}_{n-r}}\] done clear
  B)
  \[^{n}{{C}_{r}}\] done clear
  C)
  \[^{n-1}{{C}_{r}}\] done clear
  D)
  \[^{n+1}{{C}_{r}}\] done clear
  View Solution play_arrow

• question_answer36)
  If \[^{43}{{C}_{r-6}}={{\,}^{43}}{{C}_{3r+1}},\] then the value of r is [Kerala (Engg.) 2002]
  A)
  12 done clear
  B)
  8 done clear
  C)
  6 done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer37)
  How many numbers of 6 digits can be formed from the digits of the number 112233 [Karnataka CET 2004]
  A)
  30 done clear
  B)
  60 done clear
  C)
  90 done clear
  D)
  120 done clear
  View Solution play_arrow

• question_answer38)
  In an election there are 8 candidates, out of which 5 are to be choosen. If a voter may vote for any number of candidates but not greater than the number to be choosen, then in how many ways can a voter vote
  A)
  216 done clear
  B)
  114 done clear
  C)
  218 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer39)
  In an election the number of candidates is 1 greater than the persons to be elected. If a voter can vote in 254 ways, then the number of candidates is
  A)
  7 done clear
  B)
  10 done clear
  C)
  8 done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer40)
  In how many ways can 21 English and 19 Hindi books be placed in a row so that no two Hindi books are together
  A)
  1540 done clear
  B)
  1450 done clear
  C)
  1504 done clear
  D)
  1405 done clear
  View Solution play_arrow

• question_answer41)
  \[^{n}{{C}_{r}}{{+}^{n-1}}{{C}_{r}}+......{{+}^{r}}{{C}_{r}}\] = [AMU 2002]
  A)
  \[^{n+1}{{C}_{r}}\] done clear
  B)
  \[^{n+1}{{C}_{r+1}}\] done clear
  C)
  \[^{n+2}{{C}_{r}}\] done clear
  D)
  \[{{2}^{n}}\] done clear
  View Solution play_arrow

• question_answer42)
  How many words can be formed by taking 3 consonants and 2 vowels out of 5 consonants and 4 vowels
  A)
  \[^{5}{{C}_{3}}\times {{\,}^{4}}{{C}_{2}}\] done clear
  B)
  \[\frac{^{5}{{C}_{3}}\times {{\,}^{4}}{{C}_{2}}}{5}\] done clear
  C)
  \[^{5}{{C}_{3}}\times {{\,}^{4}}{{C}_{3}}\] done clear
  D)
  \[{{(}^{5}}{{C}_{3}}\times {{\,}^{4}}{{C}_{2}})\,(5)\,!\] done clear
  View Solution play_arrow

• question_answer43)
  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
  View Solution play_arrow

• question_answer44)
  In how many ways can a committee consisting of one or more members be formed out of 12 members of the Municipal Corporation
  A)
  4095 done clear
  B)
  5095 done clear
  C)
  4905 done clear
  D)
  4090 done clear
  View Solution play_arrow

• question_answer45)
  Out of 10 white, 9 black and 7 red balls, the number of ways in which selection of one or more balls can be made, is
  A)
  881 done clear
  B)
  891 done clear
  C)
  879 done clear
  D)
  892 done clear
  View Solution play_arrow

• question_answer46)
  The numbers of permutations of \[n\] things taken \[r\] at a time, when \[p\]things are always included, is
  A)
  \[^{n}{{C}_{r}}\ p\ !\] done clear
  B)
  \[^{n-p}{{C}_{r}}\ r\ !\] done clear
  C)
  \[^{n-p}{{C}_{r-p}}\ r\ !\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer47)
  Two packs of 52 cards are shuffled together. The number of ways in which a man can be dealt 26 cards so that he does not get two cards of the same suit and same denomination is
  A)
  \[^{52}{{C}_{26}}\ .\ {{2}^{26}}\] done clear
  B)
  \[^{104}{{C}_{26}}\] done clear
  C)
  \[2\ .{{\ }^{52}}{{C}_{26}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer48)
  In a touring cricket team there are 16 players in all including 5 bowlers and 2 wicket-keepers. How many teams of 11 players from these, can be chosen, so as to include three bowlers and one wicket-keeper [MP PET 1984]
  A)
  650 done clear
  B)
  720 done clear
  C)
  750 done clear
  D)
  800 done clear
  View Solution play_arrow

• question_answer49)
  Out of 6 books, in how many ways can a set of one or more books be chosen [MP PET 1984]
  A)
  64 done clear
  B)
  63 done clear
  C)
  62 done clear
  D)
  65 done clear
  View Solution play_arrow

• question_answer50)
  Choose the correct number of ways in which  15  different books can be divided into five heaps of equal number of books [MP PET 1982]
  A)
  \[\frac{15\ !}{5\ !\ {{(3\ !)}^{5}}}\] done clear
  B)
  \[\frac{15\ !}{{{(3\ !)}^{5}}}\] done clear
  C)
  \[^{15}{{C}_{5}}\] done clear
  D)
  \[^{15}{{P}_{5}}\] done clear
  View Solution play_arrow

• question_answer51)
  The number of ways of dividing 52 cards amongst four players equally, are [IIT 1979]
  A)
  \[\frac{52\ !}{{{(13\ !)}^{4}}}\] done clear
  B)
  \[\frac{52\ !}{{{(13\ !)}^{2}}\ 4\ !}\] done clear
  C)
  \[\frac{52\ !}{{{(12\ !)}^{4}}\ (4\ !)}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer52)
  How many words of 4 consonants and 3 vowels can be formed  from 6 consonants and 5 vowels [RPET 1985]
  A)
  75000 done clear
  B)
  756000 done clear
  C)
  75600 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer53)
  In the 13 cricket players 4 are bowlers, then how many ways can form a cricket team of 11 players in which at least 2 bowlers included [RPET 1988]
  A)
  55 done clear
  B)
  72 done clear
  C)
  78 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer54)
  Six '+' and four '-' signs are to placed in a straight line so that no two '-' signs come together, then the total number of ways are [IIT 1988]
  A)
  15 done clear
  B)
  18 done clear
  C)
  35 done clear
  D)
  42 done clear
  View Solution play_arrow

• question_answer55)
  The number of groups that can be made from 5 different green balls, 4 different blue balls and 3 different red balls, if at least 1 green and 1 blue ball is to be included [IIT 1974]
  A)
  3700 done clear
  B)
  3720 done clear
  C)
  4340 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer56)
  In how many ways can 6 persons be selected from 4 officers and 8 constables, if at least one officer is to be included   [Roorkee 1985; MP PET 2001]
  A)
  224 done clear
  B)
  672 done clear
  C)
  896 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer57)
  To fill 12 vacancies there are 25 candidates of which five are from scheduled caste. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, then the number of ways in which the selection can be made [RPET 1981]
  A)
  \[^{5}{{C}_{3}}{{\times }^{22}}{{C}_{9}}\] done clear
  B)
  \[^{22}{{C}_{9}}{{-}^{5}}{{C}_{3}}\] done clear
  C)
  \[^{22}{{C}_{3}}{{+}^{5}}{{C}_{3}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer58)
  In an election there are 5 candidates and three vacancies. A voter can vote maximum to three candidates, then in how many ways can he vote [MP PET 1987]
  A)
  125 done clear
  B)
  60 done clear
  C)
  10 done clear
  D)
  25 done clear
  View Solution play_arrow

• question_answer59)
  There are 9 chairs in a room on which 6 persons are to be seated, out of which one is guest with one specific chair. In how many ways they can sit [MP PET 1987]
  A)
  6720 done clear
  B)
  60480 done clear
  C)
  30 done clear
  D)
  346 done clear
  View Solution play_arrow

• question_answer60)
  Out of 6 boys and 4 girls, a group of 7 is to be formed. In how many ways can this be done if the group is to have a majority of boys [MP PET 1994]
  A)
  120 done clear
  B)
  90 done clear
  C)
  100 done clear
  D)
  80 done clear
  View Solution play_arrow

• question_answer61)
  The number of ways in which 10 persons can go in two boats so that there may be 5 on each boat, supposing that two particular persons will not go in the same boat is [Pb. CET 1999]
  A)
  \[\frac{1}{2}{{(}^{10}}{{C}_{5}})\] done clear
  B)
  \[2{{(}^{8}}{{C}_{4}})\] done clear
  C)
  \[\frac{1}{2}{{(}^{8}}{{C}_{5}})\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer62)
  The number of ways in which we can select three numbers from 1 to 30 so as to exclude every selection of all even numbers is
  A)
  4060 done clear
  B)
  3605 done clear
  C)
  455 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer63)
  A total number of words which can be formed out of the letters \[a,\ b,\ c,\ d,\ e,\ f\] taken 3 together such that each word contains at least one vowel, is
  A)
  72 done clear
  B)
  48 done clear
  C)
  96 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer64)
  The number of ways in which any four letters can be selected from the word ?CORGOO? is
  A)
  15 done clear
  B)
  11 done clear
  C)
  7 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer65)
  The total number of natural numbers of six digits that can be made with digits 1, 2, 3, 4, if all digits are to appear in the same number at least once, is
  A)
  1560 done clear
  B)
  840 done clear
  C)
  1080 done clear
  D)
  480 done clear
  View Solution play_arrow

• question_answer66)
  All possible two factors products are formed from numbers 1, 2, 3, 4, ...., 200. The number of factors out of the total obtained which are multiples of 5 is
  A)
  5040 done clear
  B)
  7180 done clear
  C)
  8150 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer67)
  The total number of ways of selecting six coins out of 20 one rupee coins, 10 fifty paise coins and 7 twenty five paise coins is
  A)
  28 done clear
  B)
  56 done clear
  C)
  \[^{37}{{C}_{6}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer68)
  The number of ways in which thirty five apples can be distributed among 3 boys so that each can have any number of apples, is
  A)
  1332 done clear
  B)
  666 done clear
  C)
  333 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer69)
  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 he will go to the garden is
  A)
  336 done clear
  B)
  112 done clear
  C)
  56 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer70)
  In how many ways can 5 red and 4 white balls be drawn from a bag containing 10 red and 8 white balls [EAMCET 1991; Pb. CET 2000]
  A)
  \[^{8}{{C}_{5}}{{\times }^{10}}{{C}_{4}}\] done clear
  B)
  \[^{10}{{C}_{5}}{{\times }^{8}}{{C}_{4}}\] done clear
  C)
  \[^{18}{{C}_{9}}\] done clear
  D)
  None of these done clear
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• question_answer71)
  \[^{14}{{C}_{4}}+\sum\limits_{j=1}^{4}{^{18-j}{{C}_{3}}}\] is equal to [EAMCET 1991]
  A)
  \[^{18}{{C}_{3}}\] done clear
  B)
  \[^{18}{{C}_{4}}\] done clear
  C)
  \[^{14}{{C}_{7}}\] done clear
  D)
  None of these done clear
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• question_answer72)
  The number of ways in which four letters of the word 'MATHEMATICS' can be arranged is given by [Kurukshetra CEE 1996; Pb. CET 1995]
  A)
  136 done clear
  B)
  192 done clear
  C)
  1680 done clear
  D)
  2454 done clear
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• question_answer73)
  10 different letters of English alphabet are given. Out of these letters, words of 5 letters are formed. How many words are formed when at least one letter is repeated [UPSEAT 1999]
  A)
  99748 done clear
  B)
  98748 done clear
  C)
  96747 done clear
  D)
  97147 done clear
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• question_answer74)
  The number of ways in which a committee  of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains at least 3 ladies is [Kerala (Engg.) 2002]
  A)
  252 done clear
  B)
  672 done clear
  C)
  444 done clear
  D)
  420 done clear
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• question_answer75)
  A person is permitted to select at least one and at most n coins from a collection of \[(2n+1)\] distinct coins. If the total number of ways in which he can select coins is 255, then n equals [AMU 2002]
  A)
  4 done clear
  B)
  8 done clear
  C)
  16 done clear
  D)
  32 done clear
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• question_answer76)
  A man has 10 friends. In how many ways he can invite one or more of them to a party [AMU 2002]
  A)
  \[10\,!\] done clear
  B)
  \[{{2}^{10}}\] done clear
  C)
  \[10\,!\,-\,1\] done clear
  D)
  \[{{2}^{10}}-1\] done clear
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• question_answer77)
  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 question. The number of choices available to him is [AIEEE 2003]
  A)
  140 done clear
  B)
  196 done clear
  C)
  280 done clear
  D)
  346 done clear
  View Solution play_arrow

• question_answer78)
  If \[^{n}{{C}_{r}}\] denotes the number of combinations of n things taken r at a time, then the expression \[^{n}{{C}_{r+1}}+{{\,}^{n}}{{C}_{r-1}}+\,2\times {{\,}^{n}}{{C}_{r}}\] equals [AIEEE 2003]
  A)
  \[^{n+2}{{C}_{r}}\] done clear
  B)
  \[^{n+2}{{C}_{r+1}}\] done clear
  C)
  \[^{n+1}{{C}_{r}}\] done clear
  D)
  \[^{n+1}{{C}_{r+1}}\] done clear
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• question_answer79)
  A student is allowed to select at most \[n\] books from a collection of \[(2n+1)\] books. If the total number of ways in which he can select one book is 63, then the value of \[n\] is    [IIT 1987; RPET 1999; Pb. CET 2003; Orissa JEE 2005]
  A)
  2 done clear
  B)
  3 done clear
  C)
  4 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer80)
  \[^{n-1}{{C}_{r}}=({{k}^{2}}-3)\,.{{\,}^{n}}{{C}_{r+1}}\] if \[k\in \] [IIT Screening 2004]
  A)
  \[[-\sqrt{3},\,\sqrt{3}]\] done clear
  B)
  \[(-\infty ,\,-2)\] done clear
  C)
  \[(2,\,\infty )\] done clear
  D)
  \[(\sqrt{3},\,2)\] done clear
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• question_answer81)
  The value of \[\sum\limits_{r=0}^{n-1}{\frac{^{n}{{C}_{r}}}{^{n}{{C}_{r}}+{{\,}^{n}}{{C}_{r+1}}}}\] equals [MP PET 2004]
  A)
  \[n+1\] done clear
  B)
  \[\frac{n}{2}\] done clear
  C)
  \[n+2\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer82)
  Out of 5 apples, 10 mangoes and 15 oranges, any 15 fruits distributed among two persons. The total number of ways of distribution [DCE 2005]
  A)
  66 done clear
  B)
  36 done clear
  C)
  60 done clear
  D)
  None of these done clear
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• question_answer83)
  The value of \[{}^{50}{{C}_{4}}+\sum\limits_{r=1}^{6}{^{56-r}{{C}_{3}}}\] is [AIEEE 2005]
  A)
  \[^{56}{{C}_{3}}\] done clear
  B)
  \[^{56}{{C}_{4}}\] done clear
  C)
  \[^{55}{{C}_{4}}\] done clear
  D)
  \[^{55}{{C}_{3}}\] done clear
  View Solution play_arrow

• question_answer84)
  If \[^{n}{{C}_{12}}={{\,}^{n}}{{C}_{6}}\], then \[^{n}{{C}_{2}}=\] [Karnataka CET 2005]
  A)
  72 done clear
  B)
  153 done clear
  C)
  306 done clear
  D)
  2556 done clear
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• question_answer85)
  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 [Kerala (Engg.) 2005]
  A)
  140 done clear
  B)
  196 done clear
  C)
  280 done clear
  D)
  346 done clear
  E)
  265 done clear
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