CBSE Class 11 Mathematics HOTs Permutations and Combinations

Question. Ten different letters of an alphabet are given words with five letters are formed from three given letters. Then the number of words which have at least one letter repeated are
(a) 69760
(b) 30240
(c) 99748
(d) None of these
Answer : A

Question. The total number of 5-digit numbers of different digits in which the digit in the middle is the largest is
(a) 3434
(b) 4563
(c) 2688
(d) 5292
Answer : D

Question. Anil have tiled his square bathroom wall with congruent square tiles. All the tiles are red, except those along the two diagonals, which are all blue. If he used 121 blue tiles, then the number of red tiles used are
(a) 900
(b) 1800
(c) 3600
(d) 7200
Answer : C

Question. The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary.
The number of words that appear before the word COCHIN is
(a) 360
(b) 192
(c) 96
(d) 48
Answer : C

Question. In an examination of 9 papers a candidate has to pass in more papers than 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. All possible 120 permutations of WDSMC are arranged in dictionary order, as if each were an ordinary five-letter word. The last letter of the 86^th word in the list, is :
(a) W
(b) D
(c) M
(d) C
Answer : B

Question. If m be the number of different words that can be formed with the letters of the word BHARAT in which B and H are never together and n be number of different words that can be formed with the letters of the words BHARAT in which words always begin with B and end with T. Then m/n is
(a) 10
(b) 20
(c) 1
(d) 2
Answer : B

Question. The number of distinct natural numbers up to a maximum of four digits and divisible by 5, which can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, each digit not occurring more than once in each number, is
(a) 1246
(b) 952
(c) 1106
(d) None of these
Answer : C

Question. How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions ?
(a) 16
(b) 36
(c) 60
(d) 180
Answer : C

Question. During a draw of lottery, tickets bearing numbers 1, 2, 3, ..., 40, 6 tickets are drawn out and then arranged in the descending order of their numbers. In how many ways, it is possible to have 4th ticket bearing number 25?
(a) ¹⁵C₃ × ²⁴C₂
(b) ¹²C₃ × ²⁰C₂
(c) ¹⁵C₃ + ²⁴C₂
(d) None of these
Answer : A

Question. Number of ways in which two Americans, two British, one Chinese, one Dutch and one Egyptian can sit on a round table so that persons of the same nationality are separated is
(a) 48
(b) 240
(c) 336
(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. 6 white and 6 black balls are distributed among ten identical urns, so that there is atleast one ball in each urn. Balls are all alike except for the colour and each box can hold any number of balls. The number of different distributions of the balls is:
(a) 26250
(b) 132
(c) 12
(d) 10
Answer : D

Question. There are three coplanar parallel lines. If any p points are taken on each the lines, the maximum number of triangles with vertices at these points is 
(a) 3p2(p – 1) + 1
(b) 3p2(p – 1)
(c) p2(4p – 3)
(d) None of these
Answer : C

Question. A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not take the same three children to the zoo more than once he finds than she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class is
(a) 12
(b) 10
(c) 60
(d) None of these
Answer : B

Question. Messages are conveyed by arranging four white, one blue, and three red flags on a pole. Flags of the same colour are alike. If a message is transmitted by the order in which the colours are arranged, the total number of messages that can be transmitted if exactly six flags are used is
(a) 45
(b) 65
(c) 125
(d) 185
Answer : D

Question. From the vertices of a regular polygon of 10 sides, the number of ways of selecting three vertices such that no two vertices are consecutive is
(a) 10
(b) 30
(c) 50
(d) 40
Answer : C

Question. In a class tournament, all participants were to play different games with one another. Two players fell ill after having played three games each. If the total number of games played in the tournament is equal to 84, the total number of participants in the beginning was equal to
(a) 10
(b) 15
(c) 12
(d) 14
Answer : B

Question. The number of ways in which 5 X's can be placed in the squares of the figure so that no row remains empty is

(a) 97
(b) 44
(c) 100
(d) 126
Answer : B

Question. 5 different objects are to be distributed among 3 persons such that no two persons get the same number of objects. Number of ways this can be done, is
(a) 60
(b) 90
(c) 120
(d) 150
Answer : B

Numeric Value Answer

Question. If N is the number of ways in which a person can walk up a stairway which has 7 steps if he can take 1 or 2 steps up the stairs at a time, then the value of N/3 is ...... .
Answer : 7

Question. If a, b, c are three natural numbers in AP such that a + b + c = 21 and if possible number of ordered triplet (a, b, c) is then the value of (λ – 5) is
Answer : 8

Question. There are 720 permutations of the digits 1, 2, 3, 4, 5, 6. Suppose these permutations are arranged from smallest to largest numerical values, beginning from 1 2 3 4 5 6 and ending with 6 5 4 3 2 1. Then the digit in unit place of number at 267th position is ...... .
Answer : 6

Question. In an international convention participants from 10 different countries were arranged in a row such that all the participants from the same country were together. Each country has different number of participants with maximum 10 participants from a country. If K is the number of ways that they can be arranged in a row then find the highest power of 10 in K
Answer : 9

Question. In a single correct match the column question, column I contain 10 questions and Column II contain 10 answers written in some arbitrary order. If the number ways a student can answer this question so that exactly 6 of his matching are correct is k, then (sum of digits of k)/2 is equal to
Answer : 9