Class 11 Mathematics Permutations and Combinations MCQs Set 08

PERMUTATIONS OF DISSIMILAR THINGS

Question. The different words that can be formed by using the letters of the word BHARAT so that these words will not contains B and H together is
(a) 360
(b) 120
(c) 240
(d) 480
Answer: (c) 240

Question. The number of arrangements that can be made by using all the letters of the word ‘MATRIX’ so that the vowels may be in the even places is
(a) 144
(b) 2880
(c) 720
(d) 5760
Answer: (a) 144

Question. The total number of 9 digit numbers which have all different digits is
(a) 9.9!
(b) 10!
(c) \( ^{10}P_9 \)
(d) \( 9^9 \)
Answer: (a) 9.9!

Question. Number of 2 digit even numbers that can be formed from the digits 1, 2, 3, 4 and 5 when repetitions are not allowed is
(a) 8
(b) 5!
(c) 26
(d) 16
Answer: (a) 8

Question. The number of numbers greater than 23000 can be formed from 1, 2, 3, 4, 5 is
(a) 120
(b) 96
(c) 91
(d) 90
Answer: (d) 90

Question. Two persons entered a Railway compartment in which 7 seats were vacant. The number of ways in which they can be seated is
(a) 30
(b) 42
(c) 720
(d) 360
Answer: (b) 42

Question. There are 8 floors on a building including the ground floor. If 4 persons enter the lift in the ground floor the number of ways in which they get down the lift if no two persons come out of the lift at the same floor is
(a) \( ^7C_4 \)
(b) \( 7^4 \)
(c) \( ^7P_4 \)
(d) \( 4^7 \)
Answer: (c) \( ^7P_4 \)

Question. The number of four digit even numbers that can be formed with 1, 2, 3, 4, 5, 6 is
(a) 125
(b) 180
(c) 120
(d) 360
Answer: (b) 180

Question. The number of ways in which the letters of the word ‘INSURANCE’ be arranged so that the vowels are never be separated is
(a) 4320
(b) 8640
(c) 21600
(d) 10300
Answer: (b) 8640

Question. The prismatic colours are arranged in a row. The number of arrangements in which Red and Blue come together is
(a) 720
(b) 360
(c) 2880
(d) 1440
Answer: (d) 1440

PROBLEMS ON DIVISIBILITY

Question. The number of 6 digited numbers which are not divisible by 5 that can be formed with the digits 4, 5, 6, 7, 8, 9 is
(a) 120
(b) 720
(c) 600
(d) 840
Answer: (c) 600

Question. The number of four digited numbers which are not divisible by 2 that can be formed from the digits 2, 3, 4, 5, 6 is
(a) 37
(b) 48
(c) 45
(d) 34
Answer: (b) 48

Question. The number of 4 digit numbers formed using the digits 1, 2, 3, 4, 5, 6, 7 which are divisible by 4 is
(a) 100
(b) 150
(c) 200
(d) 250
Answer: (c) 200

SUM OF THE NUMBERS

Question. The sum of all possible numbers greater than 2000 formed by using the digits 2, 3, 4, 5 is
(a) 93324
(b) 96324
(c) 92324
(d) 3668
Answer: (a) 93324

PERMUTATIONS WHEN REPETITIONS ARE ALLOWED & LIKE THINGS

Question. In a town the car plate numbers contain only three or four digits, not containing the digit 0. The maximum number of cars that can be numbered is
(a) 6480
(b) 7290
(c) 5862
(d) 3528
Answer: (b) 7290

Question. The number of 6 digit numbers in which all the odd digits and only odd digits appear, is
(a) \( \frac{5}{2}(6!) \)
(b) \( 6! \)
(c) \( \frac{1}{2}(6!) \)
(d) \( \frac{5!}{2} \)
Answer: (a) \( \frac{5}{2}(6!) \)

Question. Four dice are rolled. The number of possible outcomes in which atleast one die shows 2 is
(a) 1296
(b) 625
(c) 615
(d) 671
Answer: (d) 671

Question. The number of four digit numbers that can be formed with the digits 1, 2, 3, 4 and 5 in which atleast two digits are identical is
(a) \( 4^5 - 5! \)
(b) \( 5^4 - 5! \)
(c) \( 4^5 - 5 \)
(d) \( 5^4 - 5 \)
Answer: (b) \( 5^4 - 5! \)

Question. Number of arrangements of the letters of the word ‘BANANA’ in which two N’s do not appear adjacently is
(a) 40
(b) 60
(c) 80
(d) 100
Answer: (a) 40

Question. The number of four digit telephone numbers having at least one of their digits repeated is
(a) 4960
(b) 4959
(c) 10000
(d) 5040
Answer: (b) 4959

Question. A guardian with 5 wards wishes everyone of them to study either graduation in Arts or Science or Engineering. The number of ways he can make up his mind with regard to the education of his wards if everyone of them is fit for any of those branches of study is
(a) 5!
(b) 243
(c) 125
(d) 325
Answer: (b) 243

Question. The number of ways in which 7 distinct toys can be distributed among 3 children when each child is eligible to take all the toys is
(a) \( 3^7 \)
(b) \( 7^3 \)
(c) \( ^7P_3 \)
(d) \( ^7C_3 \)
Answer: (a) \( 3^7 \)

Question. The number of odd numbers lying between 40000 and 70000 that can be made from the digits 0, 1, 2, 4, 5, 7 if digits can be repeated any number of times is
(a) 1125
(b) 1296
(c) 766
(d) 655
Answer: (b) 1296

Question. A letter lock consists of 4 rings each marked with 10 different letters, the number of ways in which it is possible to make an unsuccessful attempts to open the lock is
(a) 8999
(b) 9999
(c) 4799
(d) 5689
Answer: (b) 9999

Question. 5 dice are thrown then the number of out comes in which there is atleast one three is
(a) \( 6^5 - 1 \)
(b) \( 6^5 - 5^5 \)
(c) \( 6^5 - 6.5^4 \)
(d) \( 5^5 - 1 \)
Answer: (b) \( 6^5 - 5^5 \)

Question. A library has ‘a’ copies of one book, ‘b’ copies of two books, ‘c’ copies of each of three books and single copy of d books. The total number of ways in which these books can be distributed is
(a) \( \frac{(a + 2b + 3c + d)!}{a!b!c!} \)
(b) \( \frac{(a + b + c + d)!}{a!b!c!} \)
(c) \( \frac{(a + 2b + 3c + d)!}{a!(b!)^2(c!)^3} \)
(d) \( \frac{(a + 2b + 3c + d)!}{a!(b!)^3(c!)^2} \)
Answer: (c) \( \frac{(a + 2b + 3c + d)!}{a!(b!)^2(c!)^3} \)

Question. The number of ways that the letters of the word “NELLORE” be arranged so that ‘N’ and ‘R’ are always together is
(a) 360
(b) 720
(c) 1260
(d) 2520
Answer: (a) 360

Question. The number of ways in which all the letters of the word “INTEGRATION” can be arranged so that all vowels are always in the begining of the word is
(a) \( \frac{6! 5!}{(2!)^3} \)
(b) \( \frac{7! 4!}{2!} \)
(c) \( 7! 4! \)
(d) \( \frac{7!}{(2!)^2} \)
Answer: (a) \( \frac{6! 5!}{(2!)^3} \)

Question. Number of arrangements that can be formed using the letters A thrice, B twice and C once is
(a) 60
(b) 120
(c) 90
(d) 59
Answer: (a) 60

PROBLEMS ON NUMBER OF FUNCTIONS

Question. The number of ways of 3 scholarships of unequal value be awarded to 17 candidates, such that no candidate gets more than one scholarship is
(a) \( ^{17}C_3 \)
(b) \( 17^3 \)
(c) \( 3^{17} \)
(d) \( ^{17}P_3 \)
Answer: (d) \( ^{17}P_3 \)

Question. Each of the 5 questions in multiple choice test has 4 possible answers. The number of different sets of possible answers is
(a) 1023
(b) \( 5^4 - 1 \)
(c) 1024
(d) 256
Answer: (c) 1024

PROBLEMS BASED ON RANK MODEL

Question. The letters of the word ‘ZENITH’ are permuted in all possible ways and the words thus formed are arranged as in a dictionary. The rank of the word ‘ZENITH’ is
(a) 616
(b) 618
(c) 597
(d) 5930
Answer: (a) 616

Question. The letters of the word ‘MIRROR’ are taken and permuted in all possible ways. The words thus formed are arranged as in a dictionary then the rank of the given word is
(a) 22
(b) 23
(c) 24
(d) 25
Answer: (b) 23

Question. The letters of the word ‘AEIOU’ are permuted in all possible ways and the words thus formed are arranged as in a dictionary, the rank of the word “UIOEA” is
(a) 118
(b) 116
(c) 114
(d) 120
Answer: (c) 114

Question. Four digit numbers formed with 1, 2, 4, 6, 8 without repetition are formed in ascending order, then the rank of 4618 is
(a) 31
(b) 62
(c) 124
(d) 248
Answer: (b) 62

PROBLEMS BASED ON CIRCULAR PERMUTATIONS

Question. The number of ways of arranging 8 men and 4 women around a circular table such that no two women sit together is
(a) 8!
(b) 4!
(c) 8! 4!
(d) 7! \( ^8P_4 \)
Answer: (d) 7! \( ^8P_4 \)

Question. The number of ways that the chief minister and the 14 ministers of our state can sit at a round table for a conference so that chief minister can occupy the fixed seat is
(a) 13!
(b) 14!
(c) 14!/2
(d) 15!
Answer: (b) 14!

PALINDROMES

Question. The no. of 6 letter palindromes that can be formed using the letters of the word ‘EQUATION’ are
(a) \( 8^6 \)
(b) \( 8^3 \)
(c) \( 8^5 \)
(d) \( 8^4 \)
Answer: (b) \( 8^3 \)

Question. The number of palindromes with 5 digits that can be formed using the digits 0, 1, 2, 3, 4, 5 are
(a) \( 5 \times 6^2 \)
(b) \( 5 \times 6^3 \)
(c) \( 5 \times 6^4 \)
(d) \( 5^3 \)
Answer: (a) \( 5 \times 6^2 \)

Question. Six examination papers are to be set in a certain order not to be disclosed. It is discovered that one order has been leaked out. The number of ways that their order can be changed is
(a) \( ^6\text{P}_1 \)
(b) \( ^6\text{C}_1 \)
(c) 216
(d) 719
Answer: (d) 719