PERMUTATION AND COMBINATION...PERMUTATION AND COMBINATION 3 64, CIRCULAR ROAD , LALPUR, RANCHI, MOB-7544007542/43 35. If a denotes the number of permutations of x+2 things …

PERMUTATION AND COMBINATION

1 64, CIRCULAR ROAD , LALPUR, RANCHI, MOB-7544007542/43

1. If nPr = 720 nCr, then the value of r is

(a) 6 (b) 5 (c) 4 (d) 7

2. The value of

n

r

rn

r

P

1!

is

(a) 2n (b) nn -1 (c) 2n-1 (d) 2n +1

3. If 12Pr = 11P6+6.

11P5 then r is equal to (a) 6 (b) 5 (c) 7 (d) none of these

4. If n-1C3 + n-1C4>

nC3, then

(a) n4 (b) n>5 (c) n>7 (d) none of these 5. nCr+2

nCr-1+nCr-2 is equal to

(a) n+1Cr (b) nCr+1 (c)

n-1Cr+1 (d) none of these

6. If 2 n+1 Pn-1: 2 n-1 Pn = 3:5, then n is equal to

(a) 6 (b) 6 (c) 3 (d) 8

7. If 35Cn+7=35C4 n-2, then all the values of n are given by

(a) 28 (b) 3, 6 (c) 3 (d) 6

8. If nCr-1 =36, nCr = 84 and

nCr+1 = 126, then (a) n=8, r=4(b) n=9, r=3 (c) n=7, r=5 (d) none of these

9. If n-1C6+n-1C7>

nC6, then

(a) n>4 (b) n>12 (c) n13 (d) n>13 10. Which of the following is incorrect?

(a) nCr=nCn-r (b)

nCr=n-1Cr+

nCn-r (c)nCr=

n-1Cr+n-1Cr-1 (d)r!

nCr=nPr

11. If 56Cr+6:54Pr+3=30800:1, then the value of r is

(a) 40 (b) 41 (c) 42 (d) none of these

12.

m

r

nrn C

0

is equal to

(a) n+m+1Cn+1 (b) n+m+2Cn (c)

n+m+3Cn-1 (d) none of these 13. Ever body in a room shakes hands with every body else. The total number of hand shakes

is 66. The total number of persons in the room is (a) 11 (b) 12 (c) 13 (d) 14

14. On the occasion of Dipawli festival each student of a class sends greeting cards to the

other. If there are 20 students in the class, then the total number of greeting cards exchanged by the students is

(a) 20C2 (b)2.20C2 (c) 2.

20P2 (d) none of these 15. If n+2C8:

n-2P4=57:16, then the value of n is (a) 20 (b) 19 (c) 18 (d) 17

16. The exponent of 3 in 100 ! is

(a) 33 (b) 44 (c) 48 (d) 52 17. 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

(a) 69760 (b) 3240 (c) 999748 (d) none of these 18. If 7 points out of 12 are in the same straight line, then the number of triangles formed is

(a) 19 (b) 158 (c) 185 (d) 201 19. A polygon has 44 diagonals, the number of its sides is



(a) 9 (b) 10 (c) 11 (d) 12

20. A polygon has 170 diagonals. How many sides will it have? (a) 12 (b) 17 (c) 20 (d) 25

21. The number of all possible selections of one or more questions from 10 given questions, each question having an alternative is (a) 310 (b) 210-1 (c) 310-1 (d) 210

22. The number of ways of painting the faces of a cube with six different colours is (a) 1 (b) 6 (c)6! (d) none of these

23. 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? (a) 129 (b) 84 (c) 64 (d) none of these

24. The number of different permutations of the word BANANA is (a) 720 (b) 60 (c) 120 (d) 360

25. A person wishes to make up as many different arties as he can out of his 20 friends such that each party consists of the same number of persons. The number of friends he should invite at a time is

(a) 5 (b) 10 (c) 8 (d) none of these 26. The number of ways in which 8 different flowers can be strung to form a garland so that 4

particular flowers are never separated is

(a) 4!.4! (b) !4

!8 (c) 288 (d)none of these

27. The 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 (b) 48 (c) 96 (d)none of these

28. The smallest value of x satisfying the inequality 10Cx-1>2. 10Cx is

(a) 7 (b) 10 (c) 9 (d) 8 29. The number of arrangements which can be made using all the letters of the word LAUGH,

if the vowels are adjacent, is (a) 10 (b) 24 (c) 48 (d) 120

30. The number of ways of choosing a committee of 4 women and 5 men from 10 women and 9 men, if Mr. A refuses to serve on the committee if Ms. B is a member of the committee, cannot exceed

(a) 20580 (b) 21000 (c) 21580 (d) 22000 31. If all permutations of the letters of the word AGAIN are arranged as in dictionary, then

fiftieth word is (a) NAAGI (b) NAGAI (c) NAAIG (d) NAIAG

32. The number of ways in which any four letters can be selected from the word „CORGOO‟ is (a) 15 (b) 11 (c) 7 (d) none of these

33. A five digit number divisible b 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done is (a) 216 (b) 240 (c) 600 (d) 3125

34. If 7 points out of 12 are in the same straight line, then the number of triangles formed is (a) 19 (b) 158 (c) 185 (d) 201



35. 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 t a time such that a=182 b c, then the value of x is

(a) 15 (b) 12 (c) 10 (d) 18 36. There are 4 letters and 4 directed envelope. The number of ways in which all the letters

can be put in the wrong envelope is

(a) 8 (b) 9 (c) 16 (d) none of these 37. There are 5 letters and 5 directed envelopes. The number of ways in which all the letters

can be put in wrong envelope is (a) 119 (b) 44 (c) 59 (d) 40

38. The number of ways of selecting 10 balls from unlimited number of red, black, white and

green balls is (a) 286 (b) 84 (c) 715 (d) none of these

39. The total number of different combinations of letters which can be made from the letters of the word MISSISSIPPI is (a) 150 (b) 148 (c) 149 (d) none of these

40. 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 (b) 840 (c) 1080 (d) 480 41. The total number of seven-digit numbers the sum of whose digits is even is


42. 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 43. If the permutations of a, b, c, d, e taken all together be written down in alphabetical order

as in dictionary and numbered, then the rank of the permutation debac is

(a) 90 (b) 91 (c) 92 (d) 93 44. The number of natural numbers smaller than 104, in the decimal notation of which all the

digits are different is (a) 5274 (b) 5225 (c) 4676 (d) none of these

45. If eight persons are to address a meeting, then the number of ways in which a specified

speaker is to speak before another specified speaker is (a) 2520 (b) 20160 (c) 40320 (d) none of these

46. The total number of proper divisors of 38808 is (a) 72 (b) 70 (c) 69 (d) 71

47. All possible two factors products are formed from the numbers 1, 2, 3, 4, …, 200. The

number of factors out of the total obtained which are multiples of 5 is (a) 5040 (b) 7180 (c) 8150 (d) none of these

48. In an examination there are three multiple choice questions and each question has four choices. Number of sequences in which a student can fail to get all answers correct is

(a) 11 (b) 15 (c) 80 (d) 63 49. The letters of the word RANDOM are written in all possible orders and these words are

written out as in a dictionary then the rank of the word RANDOM is

(a) 614 (b) 615 (c) 613 (d) 616



50. The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a

time is (a) 93324 (b) 66666 (c) 84844 (d) none of these

51. The sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is (a) 18 (b) 108 (c) 432 (d) none of these

52. If the letters of the word MOTHER are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MOTHER is

(a) 240 (b) 261 (c) 308 (d) 309 53. The total number of numbers greater than 1000, but not greater than 4000, that can be

formed with the digits 0, 1, 2, 3, 4 when the repetition of digits allowed is

(a) 375 (b) 374 (c) 376 (d) none of these 54. The number of ways in which 5 picturers can be hung from 7 picture nails on the wall is

(a) 75 (b) 57 (c) 2520 (d) none of these 55. The number of all four digit numbers which are divisible by 4 that can be formed from the

digits 1, 2, 3, 4 and 5 is

(a) 125 (b) 30 (c) 95 (d) none of these 56. The number of all five digit numbers which are divisible by 4 that can be formed from the

digits 0, 1, 2, 3, 4 (without repetition) is (a)36 (b) 30 (c) 34 (d) none of these

57. The number of ways in which m+n (nm+1)different things can be arranged in a row such

that no two of the n things may be together is

(a) !!

)!(

nm

nm (b) )!(

)!1!(

nm

mm

(c)

)!1(

)!!(

nm

mm (d) none of these

58. All possible two-factor products are formed from the numbers 1, 2, …, 100. The number of factors out of the total obtained which are multiple of 3 is (a) 2211 (b) 4950 (c) 2739 (d) none of these

59. 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

(a))!(

!!

nm

nm

(b)

)!(

)!1!(

nnm

mm

(c)

)!1(

!!

nm

nm (d) none of these

60. The total number of ways in which six „+‟ and four „-„ signs occur together is (a) 35 (b) 15 (c) 30 (d)none of these

61. If in a chess tournament each contestant plays once against each of the others and in all 45 games are played, then the number of participants is

(a) 9 (b) 10 (c) 15 (d)none of these 62. A five digit number divisible by 3 is to be formed using numerals 0, 1, 2, 3, 4 and 5

without repetition. The total number of ways this can be done is (a)216 (b) 240 (c) 3125 (d) 600

63. A committee of 5 is to be formed from 9 ladies and 8 men. If the committee commands a

lady majority, then the number of ways this can be done is (a) 2352 (b) 1008 (c) 3360 (d) 3486

64. The number of ordered triplets of positive integers which are solutions of the equation x+y+z =100 is (a) 6005 (b) 4851 (c) 5081 (d)none of these



65. The number of straight lines can be formed out of 10 points of which 7 are collinear

(a) 26 (b) 21 (c) 25 (d)none of these 66. The number of ways in which ten candidates A1, A2, … A10 can be ranked such that A1 is

always above A10 is

(a) 5! (b) 2(5!) (c) 10! (d) )!10(2

1

67. In Q. 66, the number of ways in which A1 and A2 are next to each other is

(a) 9! (b) 2(9!) (c) )!9(2

1 (d)none of these

68. The total number of all proper factors of 75600 is (a) 120 (b) 119 (c) 118 (d)none of these

69. The total number of ways in which 11 identical apples can be distributed among 6 children is

(a) 252 (b) 462 (c) 42 (d)none of these 70. The number of ways in which a pack of 52 cards be divided equally amongst four players

in order is

(a) 52C13 (b)52C4 (c) 4)(13!

52! (d)

!4)(13!

52!4

71. The number of ways in which 52 cards can be divided into 4 sets, three of them having 17

cards each and the fourth one having just one card

(a)3)(17!

52! (b)

3!)(17!

52!3

(c)3)(17!

51! (d)

3!)(17!

51!3

72. The total number of ways of dividing 15 things into groups of 8, 4 and 3 respectively is

(a)2)8!4!(3!

15! (b)

8!4!3!

15! (c)8!4!

15! (d) none of these

73. There are 3 copies each of 4 different books. The number of ways in which they can be arranged in a shelf is

(a)4)(3!

12! (b)

3)(4!

12! (c)

!4)(3!

12!4

(d)!3)(4!

12!3

74. The number of ways in which 12 books can be put in 3 shelves, 4 on each, is

(a)3)(4!

12! (b)

3))(4!(3!

12! (c)

!4)(3!

12!3

(d) none of these

75. The total number of ways in which 12 persons can be divided into three groups of 4 persons each is

(a)!4)(3!

12!3

(b)3)(4!

12! (c)

!3)(4!

12!3

(d)4)(3!

12!

76. The number of ways in which 12 balls can be divided between two friends one receiving 8

and the other 4, is

(a)8!4!

12! (b)8!4!

12!2! (c)8!4!2!

12! (d) none of these

77. The total number of ways in which 2 n persons can be divided into n couples is

(a) n!n!

2n! (b)n!n!

2n! (c)n)n!(2!

2n! (d) none of these

78. 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 (b) 56 (c) 37C6 (d) none of these



79. The number of ways in which thirty five apples can be distributed among 3 boys so that

each can have any numbers of apples, is (a) 1332 (b) 666 (c) 333 (d)none of these

80. 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+3C3 (b)3

1 (m+1)(2 m2 + 4 m+1)

(c)3

1 (m+1)(2 m2 + 4 m+3) (d)none of these

81. m parallel lines in a plane are intersected by a family of n parallel lines. The total number of parallelograms so formed is

(a) 4

)1)(1( nm (b) 4

mn (c)2

)1()1( nnmm (d)4

)1)(1( nmmn

82. In a plane there are 37 straight lines, of which 13 pass through the point A and 11 pass throught 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 (b) 601 (c) 728 (d)none of these 83. 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 prloved to exceed by 66 the number of games that the men played with the women. The number of participants is

(a) 6 (b) 11 (c) 13 (d)none of these 84. A parallelogram is cut by two sets of m lines parallel to its sides. The number of

parallelograms thus formed is

(a) (mC2)2 (b) 221Cm (c)

2

22Cm (d)none of these

85. There are n straight lines in a plane, no two of which are parallel, and no three pass

through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is

(a)8

)2)(1( nnn (b)6

)3)(2)(1( nnnn

(c)8

)3)(2)(1( nnnn (d) none of these

86. 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) 805 (b) 806 (c) 816 (d)none of these 87. There are five different green dyes, four different blue dyes and three different red dyes.

The total number of combinations of dyes that can be chosen taking at least one green and one blue dye is

(a) 3255 (b) 212 (c) 3720 (d)none of these 88. Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair

each. First the women choose the chairs from amongst the chairs marked 1 to 4; and

then the men select the chairs from amongst the remaining. The numbers of possible arrangements is

(a) 4C3. 4C2 (b)

4C2. 4P3 (c)

4P2. 4P3 (d)none of these



89. 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 a book is 63, then the value of n is (a) 6 (b) 3 (c) 4 (d)none of these

90. In a steamer there are stalls for 12 animals and there are cows, horses and calves (not less than 12 of each) ready to be shipped; the total number of ways in which the shipload can be made is

(a) 312 (b) 123 (c) 12P3 (d) 12C3 91. The number of numbers that can be formed by using digits 1, 2, 3, 4, 3, 2, 1 so that odd

digits always occupy odd places (a) 3!4! (b) 34 (c) 18 (d) 12

92. Number of ways in which Rs. 18 can be distributed amongst four persons such that no

body receives less than Rs.4 is (a) 42 (b) 24 (c) 4! (d)none of these

93. A box contains two white balls, three black balls and four red balls. The number of ways in which three balls can be drawn from the box, so that at least one of the ball is black is (a) 74 (b) 64 (c) 84 (d) 20

94. The number of ways in which four letters can be selected from the word degree is

(a) 7 (b) 6 (c) !3

!6 (d)none of these

95. The total number of arrangements which can be made out of the letters of the word „Algebra‟, without altering the relative position of vowels and consonants is

(a)2!

7! (b)2!5!

7! (c) 4!3! (d)2

4!3!

96. The number of ways in which seven persons can be arranged at a round table if two particular persons may not sit together is (a) 480 (b) 120 (c) 80 (d)none of these

97. The total number of ways in which 4 boys and 4 girls can form a line, with boys and girls alternating, is

(a) (41)2 (b) 8! (c) 2(4!)2 (d) 4!.5P4 98. The number of permutations of all the letters of the word „MISSISSIPPI‟ is

(a) 46504 (b) 34650 (c) 77880 (d)none of these

99. A code word consists of three letters of the English alphabet followed by two digits of the decimal system. If neither letter nor digit is repeated in any code word, then the total

number of code words is (a) 1404000 (b) 16848000 (c) 2808000 (d)none of these

100. The number of permutations of all the letters of the word „EXERCISES‟ is

(a) 60480 (b) 30240 (c) 10080 (d)none of these 101. A father with 8 children takes 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 (b) 112 (c) 56 (d)none of these 102. 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 (b) 21 (c) 112 (d)none of these



103. If the letters of the word LATE be permuted and the words so formed be arranged as in a

dictionary. Then the rank of LATE is (a)12 (b) 13 (c) 14 (d) 15

104. The total number of ways of arranging the letters AAAA BBB CC D E F in a row such that letters C are separated from one another is (a) 2772000 (b) 1386000 (c) 4158000 (d)none of these

105. 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 (b) 204 (c) 205 (d) 195

106. 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 each in a box, could be placed such that a ball does not go to a box of its own colour is

(a) 9 (b) 24 (c) 12 (d)none of these 107. The number of all the possible selections which a student can make for answering one or

more questions out of eight given questions in a paper, when each question has an

alternative is (a) 256 (b) 6560 (c) 6561 (d)none of these

108. The greatest possible number of points of intersection of 8 straight lines and 4 circles is (a) 32 (b) 64 (c) 76 (d) 104

109. A lady gives a dinner party to 5 guests to be selected from nine friends. The number of

ways of forming the party of 5, given that two of the friends will not attend the party together is

(a) 56 (b) 126 (c) 91 (d)none of these 110. There are 10 lamps in a hall. Each one of them can be switched on independently. The

number of ways in which the hall can be illuminated is

(a) 102 (b) 1023 (c) 210 (d) 10! 111. The number of ways in which four persons be seated at a round table, so that all shall not

have the same neighbours in any two arrangements is (a) 24 (b) 6 (c) 3 (d) 4

112. At an election there are five candidates and three members to be elected, and an elector

may vote for any number of candidates not greater than the number to be elected. Then the number of ways in which an elector may vote is

(a) 25 (b) 30 (c) 32 (d)none of these 113. There are n different books and p copies of each. The number of ways in which a selection

can be made from them is

(a) np (b) pn (c) (p+1)n-1 (d) (n+1)p -1

114. 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) !!!

)!(

cba

dcba (b)32 )!()!!(

)!32(

cba

dcba

(c)!!!

)!32(

cba

dcba (d)none of these



115. The total number of arrangements of the letters in the expression a3 b2 c4 when written at

full length is (a) 1260 (b) 2520 (c) 610 (d)none of these

116. The total number of selections of fruit which can be made from 3 bananas, 4 apples and 2 oranges is (a) 39 (b) 315 (c) 512 (d)none of these

117. The total number of ways of dividing mn things into n equal groups is

(a)!!

)!(

nm

mn (b)!)(

)!(

mn

mnm

(c)!)!(

)!!(

nm

nmn

(d)none of these

118. The total number of permutations of 4 letters that can be made out of the letters of the word EXAMINATION is (a) 2454 (b) 2436 (c) 2545 (d)none of these

119. Seven women and seven men are to sit round a circular table such that there is a man on either side of every women; the number of seating arrangements is

(a) (7!)2 (b) (6!)2 (c) 6!7! (d) 7! 120. 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

(a) (2n+2)! (b) (2n+2)!2 (c) (n+1)!2 (d) 2(n+1)!}2

121. 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 (a) 9(10!) (b) 2(10!) (c) 45(8!) (d) 10!

122. 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

(a) 69760 (b) 30240 (c) 99784 (d)none of these 123. The number of ways in which a team of eleven players can be selected from 22 players

including 2 of them and excluding 4 of them is

(a) 16C11 (b) 16C5 (c)

16C9 (d) 20C9

124. In a football championship, 153 matches were played. Every team played one match with

each other. The number of teams participating in the championship is (a) 17 (b) 18 (c) 9 (d)none of these

125. 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?

(a) 58P3 (b) 58C8 (c) 5!

8P3 (d) 5!8C3

126. If x, y and r are positive integers, then xCr+xCr-1

yC1+xCr-2

yC2+…+ yCr =

(a) r!

y!x! (b) r!

y)!(x (c) x+yCR (d) xyCr

127. In how many ways can 5 red and 4 white balls be drawn from a bag containing 10 red and

8 white balls

(a)8C3 10C4 (b)

10C5 8C4 (c)

18C9 (d)none of these 128. All the letters of the word „EAMCET‟ are arranged in all possible ways. The number of such

arrangements in which two vowels are adjacent to each other is (a) 360 (b) 144 (c) 72 (d) 54.

129. There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is (a) 102 (b) 1023 (c) 210 (d) 10!



130. How many 10 digits numbers can be written by using the digits 1 and 2

(a) 10C1+9C2 (b) 2

10 (c) 10C2 (d) 10! 131. The straight lines I1, I2, I3 are parallel and lie in the same plane. A total number of m

points are taken on I1; n points on I2, k points on I3. The maximum number of triangles formed with vertices at these points are (a) m+n+kC3 (b)

m+n+kC3-mC3-

nC-kC3 (c) mC3+

nC3+kC3 (d)none of these

132. The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is

(a) 6 (b) 18 (c) 12 (d) 9 133. The number of diagonals that can be drawn by joining the vertices of an octagon is

(a) 28 (b) 48 (c) 20 (d)none of these

134. The sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is

(a) 432 (b) 108 (c) 36 (d) 18 135. 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

(a) 11 (b) 12 (c) 27 (d) 63 136. There are 10 points in a plane, out of these 6 are collinear. The number of triangles

formed by joining these points is (a) 100 (b) 120 (c) 150 (d)none of these

137. Ramesh has 6 friends. In how many ways can he invite one or more of them at a dinner?

(a) 61 (b) 62 (c) 63 (d) 64 138. Let Pm stand for

mPm. Then 1+P1 +2 P2+3 P3+… +n.Pn is equal to

(a)(n-1)! (b) n! (c) (n+1)! (d) none of these

139. For 1rn, the value of nCr+n-1Cr+

n-2Cr+…+rCr is

(a) nCn+1 (b) n+1Cr (c)

n+1Cr+1 (d) none of these

140. We are required to form different words with the help of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words

which begin with I and end with R, then m1/m2 is equal to (a) 42 (b) 30 (c) 6 (d) 1/30

141. In a college examination, a candidate is required to answer 6 out of 10 questions which

are divided into two sections each containing 5 questions. Further the candidate is not permitted to attempt more than 4 questions from either of the section. The number of

ways in which he can make up a choice of 6 questions, is (a) 200 (b) 150 (c) 50 (d) 50

142. If 20Cr =20Cr-10, then

18Cr r is equal to

(a) 4896 (b) 816 (c) 1632 (d) none of these 143. If 20Cr =

20Cr+4, then rC3 is equal to


144. If 15C3r = 15Cr+3, then r is equal to

(a)5 (b) 4 (c) 3 (d) 2 145. If 20Cr+1 =

20Cr-1,then r is equal to

(a) 10 (b) 11 (c) 19 (d) 12



146. If nPr =nPr+1, and

nCr = nCr-1,then

(a) n=4, r=2(b) n=3, r=2 (c) n=4, r=3 (d) n=5, r=2 147. If 2n+1Pn-1 :

2n-1Pn, = 3:5, then n is equal to

(a) 4 (b) 5 (c) 6 (d) 7 148. If C (n, 12)= C (n, 8), then C(22, n) is equal to

(a) 213 (b) 210 (c) 252 (d) 303

149. If mC1 = nC2, then

(a) 2 m=n (b) 2 m=n (n+1) (c) 2 m=n (n-1) (d) 2 n=m (m-1)

150. If nC12 = nC8, then n =

(a) 20 (b) 12 (c) 6 (d) 30

151. If ,4)(

2)( 22 CC aaaa then a =

(a) r (b) r-1 (c) n (d) r+1

152. If ,4)(

2)( 22 CC aaaa then a =


153. The number of permutations of n different things taking r at a time when 3 particular things are to be included is

(a) n-3Pr-3 (b) n-3Pr (c)

nPr-3 (d) r! n-1Cr-3

154. 5C1 + 5C2 +

5C3 + 5C4 +

5C5 is equal to (a) 30 (b) 31 (c) 32 (d) 33

155. If nPr =720 and nCr =120, then r is equal to

(a) 3 (b) 4 (c) 5 (d) 6

156. Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to (a) 60 (b) 120 (c) 7200 (d) none of these

157. There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is

(a) 62 (b) 63 (c) 64 (d) 65 158. There persons enter a railway compartment. If there are 5 seats vacant, in how many

ways can they take these seats?

(a) 60 (b) 20 (c) 15 (d) 125 159. The number of ways in which 10 persons can sit around a circular table so that none of

them has the same neighbours in any two arrangements, is

(a) 9! (b)2

1 (9!) (c) 10! (d) 2

1 (10!)

160. The number of words that can be formed out of the letters of the word „COMMITTEE‟ is

(a) 3)(2!

9! (b)

2)(2!

9! (c)

2!

9! (d) 9!

161. In how many ways can a committee of 5 be made out of 6 men and 4 women containing

at least one women? (a) 246 (b) 222 (c) 186 (d) none of these

162. How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3?

(a) 420 (b) 360 (c) 400 (d) 300



163. In how many ways can 5 prizes be distributed among 4 boys when every boy can take

one or more prizes? (a) 1024 (b) 325 (c) 120 (d) 600

164. The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is (a) 1958 (b) 1956 (c) 16 (d) 64

165. There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is

(a) 45 (b) 40 (c) 39 (d) 38 166. The sum of all 4-digit numbers formed with the digits 1, 1, 4 and 6 is


167. There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?

(a) 72 (b) 78 (c) 42 (d) none of these 168. In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls

may be together?

(a) 5!5! (b) 5!4! (c) 2)!5(2

1 (d) )!4!5(2

1

169. The number of words from the letters of the word „BHARAT‟ in which B and H will never

come together, is (a) 360 (b) 240 (c) 120 (d) none of these

170. In how many ways can a pack of 52 cards be divided in 4 sets, three of them having 17

cards each and fourth just one card? (a) (b) (c) (d)

171. The number of ways in which 12 boys may be divided into three groups of 4 boys each is (a) 34650 (b) 5775 (c) 11550 (d) none of these

172. The number of ways in which 11 identical pencils can be distributed among 6 kids, each

one receiving at least one is (a) 168 (b) 308 (c) 252 (d) none of these

173. The number of ways in which 5 different gifts can be distributed among 10 students, if each student can receive any number of gifts is: (a) 252 (b) 105 (c) 510 (d) none of these

174. If the (n+1) numbers a, b, c, d … be all different and each of them a prime number, then the number of different factors of am b cd.. is

(a) m-2n (b) (m+1) 2n (c) (m+1) 2n -1 (d) none of these 175. The number of dissimilar terms in the expansion of (x+y+z)n is

(a) 2

)1( nn (b) 2

)2)(1( nn (c) 2

)3)(2( nn (d) none of these

176. The number of ways in which we can pack 9 different books into 5 parcels, if four of the parcels must contain 2 books each is

(a) 870 (b) 945 (c) 960 (d) 976 177. A lady gives a dinner party for five guests. The number of ways in which they may be

selected from among nine friends if two of the friends will not attend the party together is




178. The number of six letter words that can be formed using the letters of the word „ASSIST”

in which S‟s alternate with other letters is (a) 12 (b) 24 (c) 18 (d) none of these

179. The number of integral pairs (x, y) satisfying the equation x4 + 2071 =3y4 is (a) 56 (b) 120 (c) 28 (d) 91

180. If C0+C1+C2 +…+Cn = 256, then 2nC2 is equal to

(a) 30 (b) 60 (c) 120 (d) 59 181. The number of arrangements of the word “DELHI” in which E precedes I is

(a) 30 (b) 60 (c) 120 (d) 59 182. The number of positive integral solutions of the equation x+y+z+w=16 is

(a) 15C3 (b) 16C3 (c)

17C3 (d)none of these

183. The number of 5 digit numbers, divisible by 4, and lying between 20000 and 30000 and formed by using the digits 2, 3, 4, 7, 9 (repetitions allowed) is

(a) 100 (b) 125 (c) 150 (d) 75 184. The number of ways in which a host lady can invite for a party of 8 out of 12 people of

whom two do not want to attend the party together is

(a) 211C7 + 10C8 (b)

10C8 + 11C7 (c)

12C8 - 10C6 (d) none of these

185. (n+1)C2 + 2(2C2 +

3C2 + 4C2 +…+

nC2)=

(a) 6

)2)(1( nnn (b) 2

)2)(1( nnn

(c) 6

)12)(1( nnn (d) none of these

186. The number of ways in which we can arrange n ladies and n gentlemen at a round table

so that 2 ladies or 2 gentlemen may not sit next to one another is (a) (n-1)!(n-2)! (b) (n!) (n-1)! (c) (n+1)!n! (d) none of these

187. The number of ways in which the letters of the word constant can be arranged without

changing he relative positions of the vowels and consonants is (a) 360 (b) 256 (c) 444 (d) none of these

188. Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is

(a) 216 (b) 156 (c)172 (d) none of these 189. The number of six-digit numbers all the digits of which are odd is

(a) 7776 (b) 15325 (c) 46656 (d) none of these 190. The number of ways in which one can arrange 5 identical white balls and 4 identical black

balls in a row so that the black balls do not lie side by side is

(a) 15 (b) 20 (c) 625 (d) none of these 191. The number of ways in which 4n students can be distribute equally among 4 sections is

(a) !

!4

n

n (b) !!

!4

nn

n (c)

4)!(

!4

n

n (d)

4)!!(

!4

nn

n

192. The number of ways in which four sides of a regular tetrahedron can be painted with

different colours is: (a) 1 (b) 2 (c) 6 (d) 24



193. The number of way in which 8 different pearls can be used to form a necklace so that 4

particular pearls are always together is:

(a) 4!4! (b)!4

!8 (c) 288 (d) none of these

194. How many different committees of 5 can be formed from 6 men and 4 women on which

exact 3 men and 2 women serve? (a) 6 (b) 20 (c) 60 (d) 120

195. The number of ways to arrange the letters of the word CHEESE are (a) 120 (b) 240 (c) 720 (d) 6

196. Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and

5 and divisible by 4 is (a) 24 (b) 30 (c) 125 (d) 100

197. The number of ways of in which N positive signs and negative signs (N n) may be placed in a row so that no two negative signs are together, is (a) NCn (b)

N+1Cn (c) N! (d) N+1Pn

198. Six teachers and six students have to sit round a circular table such that there is a teacher between any two students. The number of ways in which they can sit is

(a) 6!6! (b) 5!6! (c) 5!5! (d) none of these 199. The number of ways in which three letters be posted in four letter boxes in a village, if all

the three letters are not posted in the same letter box, is

(a) 64 (b) 60 (c) 81 (d) 78 200. The number of ways of selecting 8 letters from 24 letters of which 8 are a, 8 are b and the

rest unlike, is given by

(a) 27 (b) 828 (c) 1027 (d) none of these 201. The number of ways in which we can select 3 numbers from 1 to 20 so as to exclude

every selection of three consecutive numbers is (a) 1140 (b) 1123 (c) 1122 (d) none of these

202. If the letters of the word KRISNA are arranged in all possible ways and these words are

written out as in a dictionary, then the rank of the word KRISNA is (a) 324 (b) 341 (c) 359 (d) none of these

203. 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 (b) 3605 (c) 455 (d) none of these

204. The sum of proper divisors of 72 (1 and 72 are excluded) is equal to (a) 195 (b) 122 (c) 194 (d) none of these

205. The number of times the digit 5 will be written when listing the integers from 1 to 1000 is (a)271 (b) 272 (c) 300 (d) none of these

206. The sum of all 4 digit numbers that can be formed by wring the digits 2, 4, 6, 8 (repetition

of digits not allowed), is (a) 133320 (b) 533280 (c) 53328 (d) none of these

HAPPY RAKSHABANDHAN

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PERMUTATION AND COMBINATION...PERMUTATION AND COMBINATION 3 64, CIRCULAR ROAD , LALPUR, RANCHI, MOB-7544007542/43 35. If a denotes the number of permutations of x+2 things …