Class 11 Mathematics Permutations and Combinations MCQs

Question. Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn + 1 - Tn = 21, then n equals
(a) 5
(b) 7
(c) 6
(d) 4

Answer :  B

Question. The probability that in a random arrangement of the letter of the word 'UNIVERSITY', the two I's do not come together is:
(a) 4/5
(b) 1/10
(c) 9/10
(d) 1/5

Answer :  A

Question. How many words beginning with T and ending with E can be made (with no letter repeated) out of the letters of the word 'TRIANGLE' ?
(a) 1440
(b) 8P6
(c) 720
(d) 722

Answer :  C

Question. Given 12 points in a plane, no three of which are collinear. Then number of line segments can be determined, are:
(a) 76
(b) 66
(c) 60
(d) 80

Answer :  B

Question. There are 10 true-false questions in a examination. Then these questions can be answered in:
(a) 100 ways
(b) 20 ways
(c) 512 ways
(d) 1024 ways

Answer :  D

Question. 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) 37C6
(b) 56
(c) 28
(d) 29

Answer :  C

Question. The number of numbers consisting of four different digits that can be formed with the digits 0, 1, 2, 3 is :
(a) 18
(b) 24
(c) 30
(d) 72

Answer :  A

Question. In how many ways can a consonants and a vowel be chosen out of the word COURAGE?
(a) ⁷C₂
(b) ⁷P₂
(c) ⁴P₁× ³P₁
(d) ⁴P₁+ ³P1

Answer :   C

Question. How many words can be formed from the letters of the word DOGMATIC, if all the vowels remain together :
(a) 4140
(b) 4320
(c) 432
(d) 43

Answer :  B

Question. Numbers lying between 999 and 10000 than can be formed from the digits 0, 2, 3, 6, 7, 8 (repetition of digits not allowed) are :
(a) 100
(b) 200
(c) 300
(d) 400

Answer :  C

Question. How many numbers of 6 digits can be formed from the digits of the number 112233?
(a) 30
(b) 60
(c) 90
(d) 120

Answer :  C

Question. The sum of all five digit numbers that can be formed using the digits 1, 2, 3, 4, 5 when repetition of digits is not allowed, is
(a) 366000
(b) 660000
(c) 360000
(d) 3999960\

Answer :  D

Question. How many 10 digit numbers can be written by using the digits 1 and 2 :
(a) 10C1 + 9C2
(b) 210
(c) 10C2
(d) 10!

Answer :  B

Question. In a test there were n questions. In the test 2n – i students gave worng answers to i questtions i = 1, 2, 3, ........n. If the total number of wrong anwers given is 2047 then n is
(a) 12
(b) 11
(c) 10
(d) None of these

Answer :  C

Question. A set contains (2n + 1) elements. If the number of subsets of this set which contain at most n elements is 4096, then the value of n is
(a) 6
(b) 15
(c) 21
(d) None of these

Answer :  D

Question. The number of numbers of 9 different non-zero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than the digit in the middle is
(a) 2 (4 !)
(b) (4 !) 2
(c) 8 !
(d) None of these

Answer :  B

Question. The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines:
(a) 6
(b) 9
(c) 18
(d) 12

Answer :  C

Question. Ten different letters of an alphabet are given, words with five letters are formed. The number of words which atleast one letter repeated is :
(a) 69760
(b) 30240
(c) 99748
(d) 37120

Answer :  A

Question. There are 10 points in a plane, out of which 4 points are collinear. The number of triangles formed with vertices as there points is:
(a) 20
(b) 120
(c) 40
(d) 116

Answer :  D

Question. In a college of 300 students, every student read 5 newspapers and every newspaper is read by 60 students. The number of newspaper is:
(a) at least 30
(b) at most 20
(c) exactly 25
(d) none of these

Answer :  C

Question. The number of ways in which 6 rings can be worn on four fingers of one hand is :
(a) 46
(b) 6C4
(c) 64
(d) 24

Answer :  C

Question. In a chess tournament where the participants were to play one game with one another, two players fell ill having played 6 games each, without playing among themselves. If the total number of games is 117, then the number of participants at the beginning was :
(a) 15
(b) 16
(c) 17
(d) 18

Answer :  A

Question. 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

Answer :  D

Question. How many arrangements can be made out of the letters of the word “ MOTHER” taken four at a time so that each arrangement contains the letter ´M´?
(a) 240
(b) 120
(c) 60
(d) 360

Answer :  A

Question. In how many ways can 10 lion and 6 tigers be arranged in a row so that no two tigers are together?
(a) 10! × 11P6
(b) 10! × 10P6
(c) 6! × 10P7
(d) 6! × 10P6

Answer :  A

Question. What is the LCM of 4!, 8!, 13! ?
(a) 13! × 8!
(b) 416!
(c) 104!
(d) 13!

Answer :  D

Question. In how many ways can a bowler take four wickets in a single 6-ball over ?
(a) 6
(b) 15
(c) 20
(d) 30

Answer :  B

Question. There are four chairs with two chairs in each row. In how many ways can four persons be seated on the chairs, so that no chair remains unoccupied ?
(a) 6
(b) 12
(c) 24
(d) 48

Answer :  C

Question. In how many ways can the letters of the word CORPORATION be arranged so that vowels always occupy even places ?
(a) 120
(b) 2700
(c) 720
(d) 7200

Answer :  D

Question. The number of rectangles excluding squares from a rectangle of size 9 × 6 is
(a) 391 "
(b) 791
(c) 842
(d) None of these

Answer :  B

Question. The number of three digit number of the form xyz such that x < y and z < y is
(a) 284
(b) 285
(c) 240
(d) 244

Answer :  C

Question. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :
(a) less than 500
(b) at least 500 but less than 750
(c) at least 750 but less than 1000
(d) at least 1000

Answer : D

Question. 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
(a) 346
(b) 140
(c) 196
(d) 280

Answer : C

Question. The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
(a) ⁸C₃
(b) 21
(c) 3⁸
(d) 5

Answer : B

Question. Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ⁹C₃ .
Statement-2: The number of ways of choosing any 3 places from 9 different places is ⁹C₃.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is false.
(c) Statement-1 is false, Statement-2 is true.
(d) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Answer : A

Question. There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is
(a) 36
(b) 66
(c) 108
(d) 3

Answer : C

Question. A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :
(a) 484
(b) 485
(c) 468
(d) 469

Answer : B

Question. There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by oining these points. Then :
(a) N ≤ 100
(b) 100 < N ≤ 140
(c) 140 < N ≤ 190
(d) N > 190

Answer : A

Question. If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is
(a) 12
(b) 6
(c) 10
(d) 9

Answer : A

Question. If ⁿ⁺²C₆ / ^n-2P₂ = 11, then n satisfies the equation :
(a) n² + n – 110 = 0
(b) n² + 2n – 80 = 0
(c) n² + 3n – 108 = 0
(d) n² + 5n – 84 = 0

Answer : C

Question. Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is :
(a) 275
(b) 510
(c) 219
(d) 256

Answer : C

Question. On the sides AB, BC, CA of a ΔABC, 3, 4, 5 distinct points (excluding vertices A, B, C) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are :
(a) 210
(b) 205
(c) 215
(d) 220

Answer : B

Question. Let A and B two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is
(a) 256
(b) 220
(c) 219
(d) 211

Answer : C

Question. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:
(a) 500
(b) 200
(c) 300
(d) 350

Answer : C

Question. The number of four letter words that can be formed using the letters of the word BARRACK is
(a) 144
(b) 120
(c) 264
(d) 270

Answer : D

Question. Let Tn be the number of all possible triangles formed by oining vertices of an n-sided regular polygon. If Tⁿ⁺¹ – T_n = 10, then the value of n is :
(a) 7
(b) 5
(c) 10
(d) 8

Answer : B

Question. At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is
(a) 5040
(b) 6210
(c) 385
(d) 1110

Answer : C

Question. The number of arrangements that can be formed from the letters a, b, c, d, e, f taken 3 at a time without repetition and each arrangement containing at least one vowel, is
(a) 96
(b) 128
(c) 24
(d) 72

Answer : A

Question. If the number of 5-element subsets of the set A= {a₁, a₂, ...., a₂₀} of 20 distinct elements is k times the number of 5-element subsets containing a₄, then k is
(a) 5
(b) 20/7
(c) 4
(d) 10/3

Answer : C

Question. The set S = {1, 2, 3, ......., 12} is to be partitioned into three sets A, B, C of equal si e.
Thus A ∪ B ∪ C = S, A∩B = B∩C = A∩C = Φ. The number of ways to partition S is
(a) 12!/(4!)³
(b) 12!/(4!)⁴
(c) 12!/3!(4!)³
(d) 12!/3!(4!)⁴

Answer : A