Class 11 Mathematics Permutations and Combinations MCQs Set 07

PROBLEMS ON NUMBER OF FUNCTIONS

Question. The number of many one functions from \( A = \{1, 2, 3\} \) to \( B = \{a, b, c, d\} \) is
(a) 64
(b) 24
(c) 40
(d) 0
Answer: (c) 40

Question. The number of onto functions that canbe defined from \( A = \{a, b, c, d, e\} \) to \( \{1, 2\} \) is
(a) 30
(b) 0
(c) 60
(d) 32
Answer: (a) 30

Question. The number of one one onto functions that can be defined from \( A = \{a, b, c, d\} \) into \( B = \{1, 2, 3, 4\} \) is
(a) 12
(b) 24
(c) 18
(d) 26
Answer: (b) 24

Question. The number of constant mappings from \( A = \{1, 2, 3, 4, \dots, n\} \) to \( B = \{a, b\} \) is
(a) \( n! \)
(b) \( n \)
(c) 2
(d) \( 2^{n} \)
Answer: (c) 2

PROBLEMS BASED ON RANK MODEL

Question. The rank of the word "MADHUR" when arranged in dictionary order is
(a) 362
(b) 360
(c) 358
(d) 356
Answer: (a) 362

Question. The letters of the word "DANGER" are permuted in all possible ways and the words thus formed are arranged as in a dictionary. The rank of the word "DANGER" is
(a) 132
(b) 133
(c) 134
(d) 135
Answer: (d) 135

Question. The letters of the word MASTER are permuted in all possible ways and the words thus formed are arranged as in a dictionary. The rank of the word STREAM is
(a) 597
(b) 480
(c) 612
(d) 285
Answer: (a) 597

Question. If the letters of the word "NARAYANA" are arranged as in a dictionary then the Rank of the given word is
(a) 511
(b) 512
(c) 513
(d) 514
Answer: (a) 511

Question. The letters of the word CRICKET are permuted in all possible ways and the words thus formed are rearranged as in a dictionary. The rank of the word CRICKET is
(a) 243
(b) 452
(c) 531
(d) 729
Answer: (c) 531

Question. All the numbers that can be formed using the digits, 1, 2, 3, 4 are arranged in the increasing order in magnitude. The rank of the number 3241 is
(a) 56
(b) 16
(c) 55
(d) 15
Answer: (a) 56

Question. All the numbers that can be formed using the digits 1, 2, 3, 4, 5 are arranged in the decreasing order of magnitude. The rank of 34215 is
(a) 58
(b) 62
(c) 96
(d) 128
Answer: (a) 58

PROBLEMS BASED ON CIRCULAR PERMUTATIONS

Question. A round table conference is to be held between 20 deligates of 20 countries. The number of ways in which they can be seated if two particular deligates are always to sit together is
(a) \( 19! \cdot 2! \)
(b) \( 18! \cdot 2! \)
(c) \( 18! \)
(d) \( 19! \)
Answer: (b) \( 18! \cdot 2! \)

Question. The number of ways in which 5 men, 5 women and 12 children can sit around a circular table so that the children are always together is
(a) \( 4! \cdot 4! \cdot 12! \)
(b) \( 11! \cdot 12! \)
(c) \( 10! \cdot 12! \)
(d) \( (12!)^{2} \)
Answer: (c) \( 10! \cdot 12! \)

Question. 20 persons are invited for a party. The different number of ways in which they can be seated at a circular table with two particular persons seated on a either side of the host is
(a) \( 19! \cdot 2! \)
(b) \( 18! \cdot 2! \)
(c) \( 20! \cdot 2! \)
(d) \( 18! \cdot 3! \)
Answer: (b) \( 18! \cdot 2! \)

Question. The number of ways in which 4 men and 4 women are to sit for a dinner at a round table so that no two men are to sit together is
(a) 576
(b) 144
(c) 36
(d) 120
Answer: (b) 144

Question. The number of ways in which 7 men can sit at a round table so that all shall not have the same neighbours in any two arrangements is
(a) 360
(b) 720
(c) 700
(d) 300
Answer: (a) 360

Question. 7 women and 7 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) \( 6! \cdot 7! \)
(d) \( 7! \)
Answer: (c) \( 6! \cdot 7! \)

Question. The number of circular permutations of 7 dissimilar things taken 5 at a time is
(a) 2520
(b) 1260
(c) 500
(d) 504
Answer: (d) 504

Question. The number of ways in which 8 red roses and 5 white roses of different sizes can be made out to form a garland so that no two white roses come together is
(a) \( \frac{8!}{2} \cdot ^{8}P_{5} \)
(b) \( \frac{7!}{2} \cdot ^{8}P_{5} \)
(c) \( \frac{7!}{2} \cdot ^{9}P_{5} \)
(d) \( 7! \cdot ^{4}P_{3} \)
Answer: (b) \( \frac{7!}{2} \cdot ^{8}P_{5} \)

Question. The number of ways that a garland can be made out of 6 red and 4 white roses of different sizes, so that all the white roses come together is
(a) 8640
(b) 4320
(c) 720
(d) 360
Answer: (a) 8640

PALINDROMES

Question. Number of 5 digit palindromes is
(a) 8100
(b) 900
(c) 90000
(d) 9000
Answer: (b) 900

Question. Number of 5 digit Even palindromes is
(a) 400
(b) 500
(c) 4000
(d) 5000
Answer: (a) 400

FUNDAMENTAL PRINCIPLE

Question. There are 5 doors to a lecture hall. The number of ways that a student can enter the hall and leave it by a different door is
(a) 20
(b) 16
(c) 19
(d) 21
Answer: (a) 20

Question. 15 buses fly between Hyderabad and Tirupati. The number of ways can a man go to Tirupati from Hyderabad by a bus and return by a different bus is
(a) 15
(b) 150
(c) 210
(d) 225
Answer: (c) 210

PROBLEMS BASED ON \( ^nP_r \) FORMULA

Question. If \( ^{(n+1)}P_5 : ^nP_5 = 3 : 2 \) then n is
(a) 8
(b) 14
(c) 10
(d) 6
Answer: (b) 14

Question. \( ^{15}P_8 = A + 8 \cdot ^{14}P_7 \)
\( \implies \) \( A = \) 
(a) \( ^{14}P_6 \)
(b) \( ^{14}P_8 \)
(c) \( ^{15}P_7 \)
(d) \( ^{15}P_9 \)
Answer: (b) \( ^{14}P_8 \)

Question. If \( ^{(m+n)}P_2 = 90 \), \( ^{(m-n)}P_2 = 30 \) then (m, n) =
(a) (10, 3)
(b) (9, 2)
(c) (8, 2)
(d) (7, 3)
Answer: (c) (8, 2)

Question. There are 50 stations on a railway line. The number of different kinds of single 2nd class tickets must be printed so as to enable a passenger to travel from one station to another station is
(a) \( ^{50}C_2 \)
(b) 2500
(c) 2450
(d) 50!
Answer: (c) 2450

Question. If \( ^nP_r = 3024 \) then (n, r) =
(a) (8, 4)
(b) (8, 3)
(c) (9, 3)
(d) (9, 4)
Answer: (d) (9, 4)

PROBLEMS BASED ON REMAINDER & OTHER MODELS

Question. The product 5. 6. 7. .........(r + 4) is divisible by
(a) (r - 2)!
(b) (r - 1)!
(c) r!
(d) (r + 1)!
Answer: (c) r!

Question. \( \frac{1}{3.1!} + \frac{1}{4.2!} + \frac{1}{5.3!} + \dots \infty = \)
(a) 1
(b) 2
(c) 1/2
(d) 3
Answer: (c) 1/2

PERMUTATIONS OF DISSIMILAR THINGS

Question. In a class of 10 students there are 3 girls. The number of ways they can be arranged in a row, so that no two girls are consecutive is k.8!, where k =
(a) 42
(b) 12
(c) 24
(d) 36
Answer: (a) 42

Question. The number of ways of arranging 6 players to throw the cricket ball so that the oldest player may not throw first is
(a) 120
(b) 600
(c) 720
(d) 175
Answer: (b) 600

Question. The number of times the digit ‘5’ will be written while listing the integers from 1 to 1000 is
(a) 271
(b) 272
(c) 300
(d) 285
Answer: (c) 300

Question. 10 men and 6 women are to be seated in a row so that no two women sit together, the number of ways they can be seated is
(a) \( 11!.10! \)
(b) \( \frac{11!}{6!5!} \)
(c) \( \frac{10!9!}{5!} \)
(d) \( \frac{11!10!}{5!} \)
Answer: (d) \( \frac{11!10!}{5!} \)

Question. 9 balls are to be placed in 9 boxes, and 5 of the balls can not fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is 
(a) 18720
(b) 18270
(c) 17280
(d) 12780
Answer: (c) 17280

Question. The total number of signals that can be made with 7 different coloured flags is
(a) 128
(b) 7
(c) 127
(d) 13699
Answer: (d) 13699

Question. In a class of 10 students, there are 3 girls A, B, C. The number of different ways that they can be arranged in a row such that no two of the three girls are consecutive is
(a) 10!
(b) 7! 8!
(c) 7! 8!/5!
(d) 7! 8! 3!/5!
Answer: (c) 7! 8!/5!

Question. The number of ways that 5 students can be sit in a row so that the tallest and shortest may not come together is
(a) 48
(b) 24
(c) 72
(d) 120
Answer: (c) 72

Question. \( S_1, S_2, ...., S_{10} \) are the speakers in a conference. If \( S_1 \) addresses only after \( S_2 \), then the number of ways the speakers address is
(a) 10!
(b) 9!
(c) 10 x 8!
(d) (10!)/2
Answer: (d) (10!)/2