Class 11 Mathematics Permutations and Combinations MCQs Set C

Question: mice were placed in two experimental groups and one control group with all group equally large. In how many ways can the mice be placed into three groups?
(a) 181/(6!)²
(b) 181/(6!)³
(c) 180/(6!)³
(d) None of these 
Answer: b

Question: The number of five-digit telephone numbers having atleast one of their digit repeated is :
(a) 90000
(b) 100000
(c) 30240
(d) 69760
Answer: d

Question: A person is permitted to select at least one and at most n coins from a collection of 2 1 n + (distinct) coins. If the total number of ways in which he can select coins is 255, then n is equal to
(a) 4
(b) 8
(c) 16
(d) 32 
Answer: a

Question: 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 in each box, could be placed such that a ball does not go to box of its own colour, is 
(a) 8
(b) 7
(c) 9
(d) None of these
Answer: c

Question: Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?
(a) 50
(b) 100
(c) 150
(d) 200 
Answer: c

Question: In the decimal system of numeration, the number of 6-digits numbers in which the digit in any place is greater than the digit to the left to it is :
(a) 210
(b) 84
(c) 126
(d) None of these
Answer: b

Question: The total number of numbers that can be formed by using all the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places, is :
(a) 3
(b) 6
(c) 9
(d) 18
Answer: d

Question: The number of ways of dividing 52 cards amongst four players so that three players have 17 cards each and the fourth players just one card, is
(a) 52!/(17!)³
(b) 52!
(c) 52!/17!!
(d) None of these 
Answer: a

Question: Let E = [ 1/3 +1/50 ] + [ 1/3 + 2/50 ] + ...... + upto 50 terms, then exponent of 2 in (E)! is :
(a) 13
(b) 15
(c) 17
(d) 19
Answer: b

Question: The total number of 9-digits numbers of different digits is :
(a) 10(9!)
(b) 8(9!)
(c) 9(9!)
(d) None of these
Answer: c

Question: The number of numbers divisible by 3 that can be formed by four different even digits is :
(a) 18
(b) 36
(c) 20
(d) None of these
Answer: b

Question: A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group.
Find the number of different ways of doing questions.
(a) 779
(b) 781
(c) 780
(d) 782 
Answer: c

Question: 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
(a) 4! 2!
(b) 11!
(c) 5! 4! 3! 2!
(d) None of these 
Answer: c

Question: 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 proved 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
Answer: c

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

Question: Let f :{ 1, 2, 3, 4, 5} → { 1,2, 3 ,4 ,4, 5} that are onto and f (x) ≠ is equal to
(a) 9
(b) 44
(c) 16
(d) None of these 
Answer: b

Question: In an steamer, there are stalls for 12 animals and there are horses, cows and calves (not less than 12 each) ready to be shipped in how many ways can the ship load be made?
(a) 3¹²-1
(b) 3¹²
(c) (12)³-1
(d) (12)³
Answer: b

Question: The number of 4-digits numbers that can be made with the digits 1, 2, 3, 4 and 5 in which at least two digits are identical, is :
(a) 45 – 5!
(b) 505
(c) 600
(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 is
(a) 6
(b) 18
(c) 12
(d) 9 
Answer: d

Question: Total 5 digit numbers divisible by 3 can be formed by using 0, 1, 2, 3, 4, 5 if repetition of digits is not allowed.
(a) 216
(b) 120
(c) 96
(d) None of these
Answer: a

Question: In an examination of 9 papers a candidate has to pass in more papers, then the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful, is
(a) 255
(b) 256
(c) 193
(d) 319
Answer: b

Question: Total 5-digit numbers divisible by 4 can be formed using 0, 1, 2, 3, 4, 5, when the repetition of digits is allowed
(a) 1250
(b) 875
(c) 1620
(d) 1000
Answer: c

Question: Total 5-digit numbers divisible by 6 can be formed using 0, 1, 2, 3, 4, 5 if repetition of digit is not allowed.
(a) 60
(b) 48
(c) 108
(d) None of these
Answer: c

Question: 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) (a +b +c +d!)!/a! b! c!
(b) (a+2b+3c+d)! /a!(b!)2(c!)³
(c) (a+2b+3c+d) /a! b! c!
(d) None of these
Answer: b

Question: The number of different matrices that can be formed with elements 0, 1, 2 or 3, each matrix having 4 elements is :
(a) 3 × 2⁴ 
(b) 2 × 4⁴
(c) 3 × 4⁴ 
(d) None of these
Answer: c

Question: Six identical coins are arranged in a row. The total number of ways in which the number of heads is equal to the number of tails is :
(a) 9
(b) 20
(c) 40
(d) 120
Answer: b

Question: A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together, is
(a) 112
(b) 140
(c) 164
(d) None of these 
Answer: b

Question: Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is
(a) 3600
(b) 3720
(c) 3800
(d) 3600 
Answer: b

Question: How many numbers greater than 1000 or equal to, but less than 4000 can be formed with the digits 0, 1, 2, 3, 4, repetition of digits being allowed :
(a) 374
(b) 375
(c) 376
(d) None of these
Answer: b

Question: The number of possible outcomes in a throw of n ordinary dice in which at least one of the dice shows an odd number is :
(a) 6^n–1
(b) 3^n–1
(c) 6ⁿ – 3ⁿ
(d) None of these
Answer: c

Question: The maximum number of points of intersection of 6 circles is
(a) 25
(b) 24
(c) 50
(d) 30 
Answer: d

Question: If 33! is divided by 2n, then the maximum value of n is equal to :
(a) 30
(b) 31
(c) 32
(d) 33
Answer: b

Question: The number of diagonals in a polygon of m sides is
(a) 1/2! m (m-5)
(b)1/2! m (m-1)
(c) 1/2!m (m-3)
(d)1/2!m(m-2) 
Answer: c

Question: The total numbers of words that can be made by writting the letters of the word PARAMETER so that no vowel is in between two consonants is :
(a) 1440
(b) 1800
(c) 2160
(d) None of these
Answer: b

Question: The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is
(a) 105
(b) 15
(c) 175
(d) 185 
Answer: d

Question: The number of triangles that can be formed by 5 points in a line and 3 points on a parallel line is
(a) ⁸C₃
(b) ⁸ C₃-⁵C₃
(c) ⁸C₃ − ⁵C₃-1
(d) None of these 
Answer: c

Question: Three boys of class X, four boys of class XI and five boys of class XII sit in a row. The total number of ways in which these boys can sit so that all the boys of same class sit together is equal to
(a) (3!)²(4!) (5!)
(b) (3!) (4!)²(5!)
(c) (3!) (4!) (5!)
(d) (3!) (4!) (5!)²
Answer: a

Question: The number of mappings (functions) from the set A = {1,2, 3 } into the set B = {1,2, 3, 4 ,5 ,6 ,7} such that f (i) ≤ f (j), whenever i< j, is
(a) 84
(b) 90
(c) 88
(d) None of these 
Answer: a

Question: A seven digit number divisible by 9 is to be formed by using 7 out of numbers {1, 2, 3, 4, 5, 6, 7, 8, 9}. The number of ways in which this can be done is
(a) 7!
(b) 2.(7)!
(c) 3.(7)!
(d) 4.7!
Answer: d

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: Total number of 4 digit number that are greater than 3000, that can be formed using the digits 1, 2, 3, 4, 5, 6 (no digit is being repeated in any number) is equal to :
(a) 120
(b) 240
(c) 480
(d) 80
Answer: b

Question: If a polygon has 44 diagonals, then the number of its sides are
(a) 11
(b) 7
(c) 8
(d) None of these 
Answer: a