
question_answer1) If the best and the worst paper never appear together, then six examination papers can be arranged in how many ways
A) 120
B) 480
C) 240
D) None of these
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question_answer2) How many numbers divisible by 5 and lying between 3000 and 4000 can be formed from the digits 1, 2, 3, 4, 5, 6 (repetition is not allowed)
A) \[\frac{n+r1}{r}\]
B) \[^{5}{{P}_{2}}\]
C) \[^{4}{{P}_{2}}\]
D) \[^{6}{{P}_{3}}\]
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question_answer3) The number of ways in which 6 rings can be worn on the four fingers of one hand is [AMU 1983]
A) \[{{4}^{6}}\]
B) \[^{6}{{C}_{4}}\]
C) \[{{6}^{4}}\]
D) None of these
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question_answer4) How many numbers can be formed from the digits 1, 2, 3, 4 when the repetition is not allowed
A) \[^{4}{{P}_{4}}\]
B) \[^{4}{{P}_{3}}\]
C) \[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}\]
D) \[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}{{+}^{4}}{{P}_{4}}\]
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question_answer5) There are 3 candidates for a post and one is to be selected by the votes of 7 men. The number of ways in which votes can be given is
A) \[{{7}^{3}}\]
B) \[{{3}^{7}}\]
C) \[^{7}{{C}_{3}}\]
D) None of these
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question_answer6) 4 buses runs between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by another bus, then the total possible ways are
A) 12
B) 16
C) 4
D) 8
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question_answer7) If \[{}^{n}{{P}_{5}}=20.\ {}^{n}{{P}_{3}}\], then \[n=\]
A) 4
B) 8
C) 6
D) 7
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question_answer8) How many words comprising of any three letters of the word UNIVERSAL can be formed
A) 504
B) 405
C) 540
D) 450
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question_answer9) If \[{}^{n}{{P}_{4}}\ :\ {}^{n}{{P}_{5}}=1:2\], then \[n=\] [MP PET 1987; RPET 1996]
A) 4
B) 5
C) 6
D) 7
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question_answer10) In how many ways can \[mn\] letters be posted in \[n\] letterboxes
A) \[{{(mn)}^{n}}\]
B) \[{{m}^{mn}}\]
C) \[{{n}^{mn}}\]
D) None of these
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question_answer11) In how many ways can 10 truefalse questions be replied
A) 20
B) 100
C) 512
D) 1024
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question_answer12) How many even numbers of 3 different digits can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is not allowed)
A) 224
B) 280
C) 324
D) None of these
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question_answer13) If \[^{n}{{P}_{5}}=9{{\times }^{n1}}{{P}_{4}}\], then the value of \[n\] is
A) 6
B) 8
C) 5
D) 9
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question_answer14) The value of \[^{n}{{P}_{r}}\] is equal to [IIT 1971; MP PET 1993]
A) \[^{n1}{{P}_{r}}+r{{\,}^{n1}}{{P}_{r1}}\]
B) \[n.{{\ }^{n1}}{{P}_{r}}{{+}^{n1}}{{P}_{r1}}\]
C) \[n{{(}^{n1}}{{P}_{r}}{{+}^{n1}}{{P}_{r1}})\]
D) \[^{n1}{{P}_{r1}}{{+}^{n1}}{{P}_{r}}\]
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question_answer15) Find the total number of 9 digit numbers which have all the digits different [IIT 1982]
A) \[9\times 9\ !\]
B) \[9\ !\]
C) 10!
D) None of these
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question_answer16) Four dice (six faced) are rolled. The number of possible outcomes in which at least one die shows 2 is
A) 1296
B) 625
C) 671
D) None of these
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question_answer17) There are 4 parcels and 5 postoffices. In how many different ways the registration of parcel can be made [MP PET 1983]
A) 20
B) \[{{4}^{5}}\]
C) \[{{5}^{4}}\]
D) \[{{5}^{4}}{{4}^{5}}\]
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question_answer18) In how many ways can 5 prizes be distributed among four students when every student can take one or more prizes [BIT Ranchi 1990; RPET 1988, 97]
A) 1024
B) 625
C) 120
D) 600
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question_answer19) In a train five seats are vacant, then how many ways can three passengers sit [RPET 1985; MP PET 2003]
A) 20
B) 30
C) 10
D) 60
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question_answer20) The product of any \[r\] consecutive natural numbers is always divisible by [IIT 1985]
A) \[r\ !\]
B) \[{{r}^{2}}\]
C) \[{{r}^{n}}\]
D) None of these
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question_answer21) The sum of the digits in the unit place of all numbers formed with the help of 3, 4, 5, 6 taken all at a time is [Pb. CET 1990]
A) 18
B) 432
C) 108
D) 144
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question_answer22) Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is
A) 20
B) 9
C) 120
D) 40
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question_answer23) The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is
A) 72
B) 96
C) 90
D) 98
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question_answer24) In how many ways can 10 balls be divided between two boys, one receiving two and the other eight balls
A) 45
B) 75
C) 90
D) None of these
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question_answer25) The sum of all 4 digit numbers that can be formed by using the digits 2, 4, 6, 8 (repetition of digits not allowed) is
A) 133320
B) 533280
C) 53328
D) None of these
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question_answer26) There are 5 roads leading to a town from a village. The number of different ways in which a villager can go to the town and return back, is [MP PET 1996]
A) 25
B) 20
C) 10
D) \[5\]
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question_answer27) In how many ways can five examination papers be arranged so that physics and chemistry papers never come together
A) 31
B) 48
C) 60
D) 72
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question_answer28) The number of ways in which first, second and third prizes can be given to 5 competitors is
A) 10
B) 60
C) 15
D) 125
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question_answer29) The number of 3 digit odd numbers, that can be formed by using the digits 1, 2, 3, 4, 5, 6 when the repetition is allowed, is [Pb. CET 1999]
A) 60
B) 108
C) 36
D) 30
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question_answer30) How many numbers of five digits can be formed from the numbers 2, 0, 4, 3, 8 when repetition of digits is not allowed [MP PET 2000; Pb. CET 2001]
A) 96
B) 120
C) 144
D) 14
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question_answer31) If \[^{12}{{P}_{r}}=1320\], then r is equal to [Pb. CET 2004]
A) 5
B) 4
C) 3
D) 2
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question_answer32) Assuming that no two consecutive digits are same, the number of n digit numbers, is [Orissa JEE 2004]
A) n!
B) 9!
C) \[{{9}^{n}}\]
D) \[{{n}^{9}}\]
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question_answer33) The numbers of arrangements of the letters of the word SALOON, if the two O's do not come together, is
A) 360
B) 720
C) 240
D) 120
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question_answer34) The number of words which can be formed from the letters of the word MAXIMUM, if two consonants cannot occur together, is
A) 4!
B) \[3\,!\,\,\times \,\,4\,!\]
C) 7 !
D) None of these
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question_answer35) In how many ways \[n\] books can be arranged in a row so that two specified books are not together
A) \[n\,!\,(n2)\,!\]
B) \[(n1)\,!\,(n2)\]
C) \[n\,!2(n1)\]
D) \[(n2)\,n!\]
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question_answer36) How many numbers lying between 500 and 600 can be formed with the help of the digits 1, 2, 3, 4, 5, 6 when the digits are not to be repeated
A) 20
B) 40
C) 60
D) 80
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question_answer37) Numbers greater than 1000 but not greater than 4000 which can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is allowed), are [IIT 1976; AIEEE 2002]
A) 350
B) 375
C) 450
D) 576
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question_answer38) The number of numbers that can be formed with the help of the digits 1, 2, 3, 4, 3, 2, 1 so that odd digits always occupy odd places, is [RPET 1988, 1991, 1992]
A) 24
B) 18
C) 12
D) 30
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question_answer39) In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together
A) \[5\,\,!\,\,\times \,\,3\,\,!\]
B) \[^{4}{{P}_{3}}\times 5\,\,!\]
C) \[^{6}{{P}_{3}}\times 5\,\,!\]
D) \[^{5}{{P}_{3}}\times 3\,!\]
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question_answer40) How many numbers less than 1000 can be made from the digits 1, 2, 3, 4, 5, 6 (repetition is not allowed)
A) 156
B) 160
C) 150
D) None of these
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question_answer41) How many words can be formed from the letters of the word COURTESY, whose first letter is C and the last letter is Y
A) \[6\ !\]
B) \[8\ !\]
C) \[2(6)\ !\]
D) \[2(7)\ !\]
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question_answer42) How many words can be made from the letters of the word DELHI, if L comes in the middle in every word
A) 12
B) 24
C) 60
D) 6
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question_answer43) How many numbers consisting of 5 digits can be formed in which the digits 3, 4 and 7 are used only once and the digit 5 is used twice
A) 30
B) 60
C) 45
D) 90
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question_answer44) In how many ways 3 letters can be posted in 4 letterboxes, if all the letters are not posted in the same letterbox
A) 63
B) 60
C) 77
D) 81
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question_answer45) The number of 5 digit telephone numbers having at least one of their digits repeated is [Pb. CET 2000]
A) 90,000
B) 100,000
C) 30,240
D) 69,760
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question_answer46) How many words can be formed with the letters of the word MATHEMATICS by rearranging them [MP PET 1984; DCE 2001]
A) \[\frac{11\ !}{2\ !\ 2\ !}\]
B) \[\frac{11\ !}{2\ !}\]
C) \[\frac{11\ !}{2\ !\ 2\ !\ 2\ !}\]
D) \[11\ !\]
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question_answer47) The number of arrangements of the letters of the word CALCUTTA [MP PET 1984]
A) 2520
B) 5040
C) 10,080
D) 40,320
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question_answer48) How many numbers, lying between 99 and 1000 be made from the digits 2, 3, 7, 0, 8, 6 when the digits occur only once in each number [MP PET 1984]
A) 100
B) 90
C) 120
D) 80
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question_answer49) In a circus there are ten cages for accommodating ten animals. Out of these four cages are so small that five out of 10 animals cannot enter into them. In how many ways will it be possible to accommodate ten animals in these ten cages [Roorkee 1989]
A) 66400
B) 86400
C) 96400
D) None of these
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question_answer50) How many words can be made from the letters of the word COMMITTEE [RPET 1986; MP PET 2002]
A) \[\frac{9\ !}{{{(2\ !)}^{2}}}\]
B) \[\frac{9\ !}{{{(2\ !)}^{3}}}\]
C) \[\frac{9\ !}{2\ !}\]
D) \[9\ !\]
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question_answer51) 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 is not allowed in any number [RPET 1990]
A) 60
B) 12
C) 120
D) 24
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question_answer52) The letters of the word MODESTY are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MODESTY is
A) 5040
B) 720
C) 1681
D) 2520
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question_answer53) 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 \[x11\] things taken all at a time such that \[a=182\ bc\], then the value of \[x\] is
A) 15
B) 12
C) 10
D) 18
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question_answer54) All possible four digit numbers are formed using the digits 0, 1, 2, 3 so that no number has repeated digits. The number of even numbers among them is
A) 9
B) 18
C) 10
D) None of these
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question_answer55) The number of ways in which ten candidates \[{{A}_{1}},\ {{A}_{2}},\ .......{{A}_{10}}\] can be ranked such that \[{{A}_{1}}\] is always above \[{{A}_{10}}\] is
A) \[5\ !\]
B) \[2(5\ !)\]
C) \[10\ !\]
D) \[\frac{1}{2}(10\ !)\]
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question_answer56) All the letters of the word ?EAMCET? are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is [EAMCET 1987; DEC 2000]
A) 360
B) 114
C) 72
D) 54
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question_answer57) In how many ways can 5 boys and 5 girls stand in a row so that no two girls may be together [RPET 1997]
A) \[{{(5\ !)}^{2}}\]
B) \[5\ !\ \times 4\ !\]
C) \[5\ !\ \times 6\ !\]
D) \[6\times 5\ !\]
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question_answer58) The total number of permutations of the letters of the word ?BANANA? is [RPET 1997, 2000]
A) 60
B) 120
C) 720
D) 24
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question_answer59) The number of words which can be made out of the letters of the word MOBILE when consonants always occupy odd places is [RPET 1999]
A) 20
B) 36
C) 30
D) 720
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question_answer60) How many numbers greater than 24000 can be formed by using digits 1, 2, 3, 4, 5 when no digit is repeated [RPET 1999]
A) 36
B) 60
C) 84
D) 120
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question_answer61) How many numbers greater than hundred and divisible by 5 can be made from the digits 3, 4, 5, 6, if no digit is repeated [AMU 1999]
A) 6
B) 12
C) 24
D) 30
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question_answer62) The number of 7 digit numbers which can be formed using the digits 1, 2, 3, 2, 3, 3, 4 is [Pb. CET 1999]
A) 420
B) 840
C) 2520
D) 5040
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question_answer63) The number of 4 digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contain digit 1 is [AMU 2001]
A) 1225
B) 1252
C) 1522
D) 480
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question_answer64) The number of 4 digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is [Kerala (Engg.) 2001]
A) 120
B) 300
C) 420
D) 20
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question_answer65) Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 are [AIEEE 2002]
A) 216
B) 375
C) 400
D) 720
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question_answer66) The number of arrangements of the letters of the word BANANA in which two N?s do not appear adjacently is [IIT Screening 2002]
A) 40
B) 60
C) 80
D) 100
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question_answer67) The number of ways in which 5 boys and 3 girls can be seated in a row so that each girl in between two boys [Kerala (Engg.) 2002]
A) 2880
B) 1880
C) 3800
D) 2800
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question_answer68) Eleven books consisting of 5 Mathematics, 4 Physics and 2 Chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books of the same subject are all together is [AMU 2002]
A) 4! 2!
B) 11!
C) 5! 4! 3! 2!
D) None of these
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question_answer69) The number of words that can be formed out of the letters of the word ARTICLE so that the vowels occupy even places is [Karnataka CET 2003]
A) 36
B) 574
C) 144
D) 754
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question_answer70) The number of ways in which 9 persons can be divided into three equal groups is [Orissa JEE 2003]
A) 1680
B) 840
C) 560
D) 280
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question_answer71) If a man and his wife enter in a bus, in which five seats are vacant, then the number of different ways in which they can be seated is [Pb. CET 2004]
A) 2
B) 5
C) 20
D) 40
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question_answer72) If the letters of the word SACHIN arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number [AIEEE 2005]
A) 603
B) 602
C) 601
D) 600
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question_answer73) Let the eleven letters \[A,B\].....,K denote an arbitrary permutation of the integers (1, 2,.....11), then \[(A1)(B2)(C3).....(K11)\] [Orissa JEE 2005]
A) Necessarily zero
B) Always odd
C) Always even
D) None of these
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question_answer74) 4 Note of Rs. 100 and 5 note in which first of Rs. 1, second of Rs. 2, Third of Rs. 5, fourth of Rs. 20 and fifth one of Rs. 50 distributed in 3 children such that each child receive at least one note of Rs. 100. The total number of ways of distribution [DCE 2005]
A) \[3\times {{5}^{3}}\]
B) \[5\times {{3}^{5}}\]
C) \[{{3}^{6}}\]
D) None of these
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question_answer75) How many numbers lying between 999 and 10000 can be formed with the help of the digit 0,2,3,6,7,8 when the digits are not to be repeated [AMU 2005]
A) 100
B) 200
C) 300
D) 400
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