Class 11 Mathematics Permutations and Combinations MCQs Set 02

Question: The number of ways in which 10 different diamonds can be arranged to form a necklace, is
a) 181440
b) 161400
c) 261960
d) None of the options
Answer: a

Question:

a) 4
b) 3
c) 2
d) 1
Answer: a

Question: A letter lock contains 5 rings each marked with for different letters.The number of all possible unsuccessful attempts to open the lock is
a) 625
b) 1024
c) 624
d) 1023 
Answer: b

Question:The letters of the word RACHIT are written in all possible manner and words are written as in dictionary. The rank of word RACHIT is
a) 365
b) 702
c) 481
d) 480
Answer: c

Question: There are 4 parcels and 5 post offices. In how many ways can 4 parcels be got registered?
a) 20
b) 4⁵
c) 5⁴
d) 5⁴-4 ⁵
Answer: c

Question:

a) 2⁷ -1
b) 2⁸ -2
c) 2⁸ -1
d) 2⁸
Answer: b

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: Seven different lecturers are to deliver lectures in seven periods of a class on a particular day. A B, and C are three of the lecturers. The umber of ways in which a routine for the day can be made such that A delivers his lecture before B and B before C, is
a) 420
b) 120
c) 210
d) 840
Answer: d

Question: If a represents the number of permutations of (x + 2) things taken together b represents the number of permutation of 11 things taken together out of x things, and c represents the number of permutation of(x – 11)things taken together so that a= 182,bc = then x is equal to
a) 15
b) 12
c) 10
d) 18
Answer: b

Question: A person wishes to make up as many different parties as he can out of 20 friends. Each party consists of the same number of friends. How many should be invited at a time ?
a) 8
b) 9
c) 10
d) 11
Answer: c

Question: If 1/6! +1/7!=x/8!’ then the value of x is
a) 63
b) 64
c) 66
d) 65
Answer: b

Question: A bag contains 3 black, 4 white and 2 red balls, all the ballsbeing different. Number of selections of atmost 6 balls containing balls of all the colours is
a) 1008
b) 1080
c) 1204
d) 1130
Answer: a

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

Question: The number of ways in which 7 pictures can be hung from 5 picture nails on the wall is
a) 7⁵
b) 5⁷
c) 2520
d) None of the options
Answer: c

Question: Given 5 flags of different colours, how many different signals can be generated, if each signal requires the use of 2 flags, one below the other.
a) 18
b) 20
c) 19
d) 23
Answer: b

Question: Total number of divisors of 5880 is equal to
a) 48
b) 24
c) 96
d) 16
Answer: a

Question: The total number of 9-digit numbers which have all different digits is
a) 10!
b) 9!
c) 9 9 × !
d) 10x 10 !
Answer: c

Question: How many numbers of 4-digits can be formed by using the digits 1 2 3 4 5 6 7 if atleast one digit is repeated ?
a) ⁷P₄
b) 7⁴
c) 7⁴ – ⁷p₄
d) None of the options
Answer: c

Question: The total number of ways in which 9 different boys can be distributed among three different children, so that the youngest gets 4, the middle gets 3 and the oldest gets 2, is
a) 137
b) 236
c) 1240
d) 1260
Answer: d

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: How many 5-digit telephone numbers can be constructed using the digits 0 to 9, if each number starts with 67 and no digit appears more than once?
a) 336
b) 337
c) 335
d) None of the options
Answer: a

Question: The number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains atleast 3 ladies is
a) 252
b) 672
c) 444
d) 420
Answer: a

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

Question: From a committee of 8 persons, in how many ways can we choose a chairman and a vice-chairman assuming one person cannot hold more than one position?
a) 54
b) 55
c) 52
d) 56
Answer: d

Question: If ⁿC₉ = ⁿC₈, what is the value of ⁿC₁₇ ?
a) 1
b) 0
c) 3
d) 17
Answer: a

Question: There are 6 letters and 6 directed envelopes. Find the number of ways in which all letters are put in the wrong envelopes.
a) 260
b) 265
c) 270
d) 275
Answer: b

Question: Eight straight lines are drawn in the plane such that no two lines are parallel and no three lines are concurrent. The number of parts into which these lines divide the plane, is
a) 29
b) 32
c) 36
d) 37
Answer: d

Question: If ⁵ P_r=2⁶pr-1, then the value of r is
a) 10
b) 3
c) 0
d) None of the options
Answer: b

Question: The number of ways in which four letters of the word MATHEMATICS can be arranged is given by
a) 136
b) 192
c) 1680
d) 2454
Answer: d

Question: Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are
a) 216
b) 375
c) 400
d) 720
Answer: d

Question: The number of products that can be formed with 10 prime numbers taken two or more at a time is
a) 2¹⁰
b) 2¹⁰-1
c) 2¹⁰-11
d) 2¹⁰– 10
Answer: c

Question: The number of non-negative integral solutions of x + y+z≤ n,where n∈ N is
a) n+³ C₃
b) n+⁴ C₄
c) n+⁵ C₅
d) n+² C₂
Answer: a

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 the options
Answer: b

Question: The exponent of 3 in 100! is
a) 47
b) 48
c) 49
d) 50
Answer: c

Question:The number of ways in which four particular persons A, B, C, D , and six more persons can stand in a queue so that A always stands before B B, before C and C before D, is
a) 7! 4!
b) 10! -7! 4!
c) 10!/4!
d) None of the options
Answer: c

Question: How many ways can 6 coins be chosen from 20, one rupees coins, 10 fifty paise coins, 7 twenty paise coins ?
a) 28
b) 56
c) ³⁷C6
d) 38
Answer: a

Question: On the occasion of Deepawali festival, each student of a class sends greeting cards to the others. If there are 20 students in the class, then the total number of greeting cards exchanged by the students is
a) ²⁰C₂
b) 2 . ²⁰C₂
c) 2.²⁰p₂
d) None of the options
Answer: b

Question: The value of 2ⁿ [1·3· 5…(2n-3)2n-1) is
a) (2n )!/ n!
b) (2n))! /2ⁿ
c) n!/( 2n)!
d) None of the options
Answer: a

Question: The products of any r consecutive natural numbers is always divisible by
a) r!
b) r²
c) rⁿ
d) None of the options
Answer: a

Question: If a secretary and a joint secretary are to be selected from acommittee of 11 members, then in how many ways can they be selected ?
a) 110
b) 55
c) 22
d) 11
Answer: b

Question: There were two women participants in a chess tournament. The number of games the men played between themselves exceeded by 52 the number of games they played with women. If each player played one game with each other, the number of men in the tournament, was
a) 10
b) 11
c) 12
d) 13
Answer: d

Question: Match the terms given in column-I with the terms given in column-II and choose the correct option from the codes given below.

Codes
   A B C D
a) 4 3 2 1
b) 3 4 1 2
c) 4 2 3 1
d) 3 4 2 1
Answer: d

ASSERTION – REASON TYPE QUESTIONS

a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
c) Assertion is correct, reason is incorrect
d) Assertion is incorrect, reason is correct.

Question: Assertion : If the letters W, I, F, E are arranged in a row in all possible ways and the words (with or without meaning) so formed are written as in a dictionary, then the word WIFE occurs in the 24th position.
Reason : The number of ways of arranging four distinct objects taken all at a time is C(4, 4).
Answer: c

Question: Assertion : A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 with repetition. The total number formed are 216.
Reason : If sum of digits of any number is divisible by 3 then the number must be divisible by 3.
Answer: d

Question: Assertion : A number of four different digits is formed with the help of the digits 1, 2, 3, 4, 5, 6, 7 in all possible ways. Then, number of ways which are exactly divisible by 4 is 200.
Reason : A number divisible by 4, if unit place digit is divisible by 4.
Answer: c

Question: Assertion : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ⁹C₃.
Reason : The number of ways of choosing any 3 places, from 9 different places is ⁹C₃.
Answer: a

Question: Assertion : Product of five consecutive natural numbers is divisible by 4!.
Reason : Product of n consecutive natural numbers is divisible by (n + 1)!
Answer: c