MCQs For NCERT Class 11 Maths Permutations and Combinations with Answers

Please refer to the MCQ Questions for Class 11 Permutations and Combinations Maths with Answers. The following Permutations and Combinations Class 11 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 11. Our experts have designed MCQ Questions for Class 11 Permutations and Combinations with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 11 Mathematics

Permutations and Combinations Class 11 MCQ Questions with Answers

See below Permutations and Combinations Class 11 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

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

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

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)

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) ⁸C₃ – ⁵C₃ 
(c) ⁸C₃ – ⁵C₃ – 1
 (d) None of these

Question. The straight lines I I I 1 2 3 , , are parallel and lie in the same plane. A total numbers of m points are taken on I n 1, points on I k 2, points on I3. The maximum number of triangles formed with vertices at these points is
(a) m + n + kC3
(b) m + n + kC3 – ^mC₃ – ⁿC₃ – ^kC₃
(c) ^mC₃ + ⁿC₃ + ^kC₃
(d) None of the above

Question. Six points in a plane be joined in all possible ways by indefinite straight lines and if no two of them be coincident or parallel and no three pass through the same point (with the exception of the original 6 points). The number of distinct points or intersection is equal to
(a) 105
(b) 45
(c) 51
(d) None of these

Question. The greatest possible number of points of intersection of 8 straight lines and 4 circles is
(a) 32
(b) 64
(c) 76
(d) 104

Question. There are n distinct points on the circumference of a circle. The number of pentagons that can be formed with these points as vertices is equal to the number of possible triangles. Then, the value of n is
(a) 7
(b) 8
(c) 15
(d) 30

Question. The number of divisors of 9600 including 1 and 9600 are
(a) 60
(b) 58
(c) 48
(d) 46

Question. Number of divisors of the form (4n + 2), n ≥ 0 of the integer 240 is
(a) 4
(b) 8
(c) 10
(d) 3

Question. The number of divisors of the number of 38808 (excluding 1 and the number itself ) is
(a) 70
(b) 72
(c) 71
(d) None of these

Question. If a, b, c, d, e are prime integers, then the number of divisors of ab c de 2 2 excluding 1 as a factor is
(a) 94
(b) 72
(c) 36
(d) 71

Question. The number of ordered triplets of positives integers which are solutions of the equation x + y + z = 100, is
(a) 6005
(b) 4851
(c) 5081
(d) None of these

Question. Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to 
(a) 60
(b) 120
(c) 7200
(d) 720

Question. There are 5 historical monuments, 6 gardens and 7 shopping malls in the city. In how many ways a tourist can visit the city, if he visits atleast one shopping mall?
(a) 2⁵.2⁶( 2⁷ – 1)
(b) 2⁴.2⁶( 2⁷ – 1)
(c) 2⁵.2⁶( 2⁶ – 1)
(d) None of these

Question. In a city no two persons have identical set of teeth and there is no person without a tooth. Also, no person has more than 32 teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, the maximum population of the city is
(a) 2³²
(b) (32)² – 1
(c) 2³² -1
(d) 2^{32 – 1}

Question. A rectangle with sides 2m – 1 and 2 n – 1 divided into squares of unit length. The number of rectangle which can be formed with sides of odd length is
(a) m²n²
(b) mn (m + 1) (n + 1)
(c) 4^{m + n – 1}
(d) None of these

Question. How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?
(a) 120
(b) 240
(c) 360
(d) 480 

Question. The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by 
(a) 6! x 5!
(b) 30
(c) 5! x 4!
(d) 7! x 5!

Question. The lock of a safe consists of five discs each of which features the digits 0, 1, 2, …, 9. The safe can be opened by dialing a special combination of the digits.
The number of days sufficient enough to open the safe. If the work day lasts 13 h and 5 s are needed to dial one combination of digits is
(a) 9
(b) 10
(c) 11
(d) 12

Question. The interior angles of a regular polygon measure 160° each. The number of diagonals of the polygon are
(a) 97
(b) 105
(c) 135
(d) 146

Question. Let A be the set of 4-digit numbers a1, a2, a3, a4, where a1 < a2 < a3 < a4, then n (A) is equal to
(a) 84
(b) 126
(c) 210
(d) None of these

Question. If the total number of m elements subsets of the set { a1, a2, a3….. a4} λ is l times the number of 3 elements subsets containing a4, then n is
(a) (m – 1) λ
(b) mλ
(c) (m + 1) λ
(d) 0

Question. Sixteen men compete with one another in running,swimming and riding. How many prize lists could be made, if there were altogether 6 prizes of different values, one for running, 2 for swimming and 3 for riding?
(a) 16 x 15 x 14
(b) 16³ x 15² x 14
(c) 16³ x 15 x 14² 
(d) 16² x 15 x 14

Question. The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is
(a) 27378
(b) 27405
(c) 27399
(d) None of these

Question. The number of different seven digit numbers that can be written using only the three digits 1, 2 and 3 with the condition that the digit 2 occurs twice in each number is
(a) ⁷P₂2
(b) ⁷P₂2⁵
(c) ⁷P₂2⁵ 
(d) None of these

Question. If the difference of the number of arrangements of three things from a certain number of dissimilar things and the number of selections of the same number of things from them exceeds 100, then the least number of dissimilar things is
(a) 8
(b) 6
(c) 5
(d) 7

Question. In how many different ways can the first 12 natural numbers be divided into three different groups such that numbers in each group are in AP?
(a) 1
(b) 5
(c) 6
(d) 4

Question. Two packs of 52 cards are shuffled together. The number of ways in which a man can be dealt 20 cards, so that he does not get two cards of the same suit and same denomination is
(a) ⁵⁶C₂₀ x 2²⁰
(b) ¹⁰⁴C₂₀
(c) 2 x ⁵²C₂₀
(d) None of these

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

Question. A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is
(a) 140
(b) 196
(c) 280
(d) 346

Question. The rank of the word ‘SUCCESS’ in the dictionary is
(a) 328
(b) 329
(c) 330
(d) 331

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

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

Question. Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is
(a) 880
(b) 629
(c) 630
(d) 879

Question. Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can formed such that Y Í X, Z Í X and Y Ç Z is empty, is
(a) 5 2
(b) 35
(c) 25
(d) 53

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) 3
(b) 36
(c) 66
(d) 108

Question: The straight lines I₁, I₂, I₃ are parallel and lie in the same plane. A total numbers of m points are taken on I₁,n,points on I₂, k ,points on I₃· The maximum number of triangles formed with vertices at these points is b

Question: The greatest possible number of points of intersection of 8 straight lines and 4 circles is
(a) 32
(b) 64
(c) 76
(d) 104 

Question:There are n distinct points on the circumference of a circle. The number of pentagons that can be formed with these points as vertices is equal to the number of possible triangles. Then, the value of n is 
(a) 7
(b) 8
(c) 15
(d) 30 

Question. A sequence is a ternary sequence, if it contains digits 0, 1 and 2. The total number of ternary sequences of length 9 which either begin with 210 or end with 210, is
(a) 1458
(b) 1431
(c) 729
(d) 707

Question.

(a) 100
(b) 110
(c) 99
(d) 121

Question. In a football championship, 153 matches were played. Every two teams played one match with each other. The number of teams, participating in the championship is ……… .
(a) 18
(b) 17
(c) 16
(d) 10

Question. The number of ways of arranging seven persons (having A, B, C and Damong them) in a row, so that A, B, C and D are always in order A-B-C-D (not necessarily together) is
(a) 210
(b) 5040
(c) 6 x ⁷C₃
(d) ⁷P3   

Question. Total number of ways of giving atleast one coin out of three 25 paise and two 50 paise coins to a beggar is
(a) 32
(b) 12       
(c) 11
(d) ¹²P₁ – 1

Question. P(n − 1 , r) + r ×P (n − 1 , r − 1 ) equals
(a) P(n − 1, r + 1)
(b) P(n , r − 1)
(c) P(n , r)
(d) P(n + 1, r + 1)

Question. ^{n – 1}P₃ : ⁿP₄ = 1 : 9 then n equals.
(a) 1
(b) 8
(c) 9
(d) 16

Question. Find the number of 4 letter words, with or without meaning, which can be formed out of letter of word ‘ROSE’. When repetition of the letters is allowed are 260.
(a) 24
(b) 256
(c) 36
(d) 12

Question: Six points in a plane be joined in all possible ways by indefinite straight lines and if no two of them be coincident or parallel and no three pass through the same point (with the exception of the original 6 points). The number of distinct points or intersection is equal to
(a) 105
(b) 45
(c) 51
(d) None of these 

Question: Number of divisors of the form (4n+2),n ≥ 0 of the integer 240 is
(a) 4
(b) 8
(c) 10
(d) 3 

Question: The number of divisors of 9600 including 1 and 9600 are
(a) 60
(b) 58
(c) 48
(d) 46 

Question: If a, b,c, d, e are prime integers, then the number of divisors of ab² c² de excluding 1 as a factor is
(a) 94
(b) 72
(c) 36
(d) 71   

Question: The number of ways can 10 letters be placed in 10 marked envelopes, so that no letter is in the right envelope are

Question: The number of ordered triplets of positives integers which are solutions of the equation x+ y+ z+ = 100, is
(a) 6005
(b) 4851
(c) 5081
(d) None of these 

Question: The number of divisors of the number of 38808 (excluding 1 and the number itself ) is
(a) 70
(b) 72
(c) 71
(d) None of these 

Question: There are 5 historical monuments, 6 gardens and 7 shopping malls in the city. In how many ways a tourist can visit the city, if he visits atleast one shopping mall?
(a) 2⁵⋅2⁶⋅ (2⁷-1)
(b) 2⁴⋅2⁶ (2⁷-1 )
(c) 2⁵⋅ 2⁶(2⁶-1)
(d) None of these 

Question: In a city no two persons have identical set of teeth and there is no person without a tooth. Also, no person has more than 32 teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, the maximum population of the city is
(a) 2³²
(b) (32)²-1
(c) 2³²-1 
(d) 2^{32- 1} 

Question: A rectangle with sides 2m − 1and 2n −1 divided into squares of unit length. The number of rectangle which can be formed with sides of odd length is
(a) m² n² 
(b) mn (m+ n) (n+1 ) 
(c) 4^{m+n+− 1}
(d) None of these 

Question: Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants
is equal to 
(a) 60
(b) 120
(c) 7200
(d) 720 

Question: The interior angles of a regular polygon measure 160° each. The number of diagonals of the polygon are
(a) 97
(b) 105
(c) 135
(d) 146   

Question: The lock of a safe consists of five discs each of which features the digits 0,1,2,… 9 .The safe can be opened by dialing a special combination of the digits.
The number of days sufficient enough to open the safe. If the work day lasts 13 h and 5 s are needed to dial one combination of digits is
(a) 9
(b) 10
(c) 11
(d) 12 

Question: If the total number of m elements subsets of the set A ={a₁,a₂,a₃,…., a_n} is  λ times the number of 3 elements subsets containing a₄, then n is
(a) (m −1) λ 1
(b) mλ
(c) (m+1) λ 
(d) 0 

Question: Let A be the set of 4-digit numbers a₁ a₂ a₃ a₄   where a1< a₂ <a₃< a₄,then n (A) is equal to
(a) 84
(b) 126
(c) 210
(d) None of these 

Question: Sixteen men compete with one another in running,swimming and riding. How many prize lists could be made, if there were altogether 6 prizes of different values, one for running, 2 for swimming and 3 for riding?
(a) 16x 15 x 14 
(b) 16³x 15²x 14 
(c) 16³x 15x 14² 
(d) 16₂x 15 x14 

Question: The number of different seven digit numbers that can be written using only the three digits 1, 2 and 3 with the condition that the digit 2 occurs twice in each number is
(a) ⁷p₂²
(b) ⁷C₂2⁵
(c) 7C₂5²
(d) None of these 

Question: The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is
(a) 27378
(b) 27405
(c) 27399
(d) None of these 

Question: A person always prefers to eat ‘parantha’ and ‘vegetable dish’ in his meal. How many ways can he make his platter in a marriage party, if there are three types of paranthas, four types of ‘vegetable dish’, three types of ‘salads’ and two types of ‘sauces’?
(a) 3360
(b) 4096
(c) 3000
(d) None of these 

Question: If the difference of the number of arrangements of three things from a certain number of dissimilar things and the number of selections of the same number of things from them exceeds 100, then the least number of dissimilar things is
(a) 8
(b) 6
(c) 5
(d) 7 

Question: There are three coplanar parallel lines. If any p points are taken on each of the lines, the maximum number of triangles with vertices on these points is
(a) 3P²(P-1)+1
(b) 3P² (P-1)
(c) p²(4P-3)
(d) None of these

Question: Two packs of 52 cards are shuffled together. The number of ways in which a man can be dealt 20 cards, so that he does not get two cards of the same suit and same denomination is
(a) 56C₂₀x2²⁰
 (b)¹⁰⁴C₂₀
(c) 2x⁵² C₂₀
(d) None of these

Question: In how many different ways can the first 12 natural numbers be divided into three different groups such that numbers in each group are in AP?
(a) 1
(b) 5
(c) 6
(d) 4 

Question: The number of ways of arranging seven persons (having A, B, C and D among them) in a row, so that A ,B .C and D are always in order A- B- C- D (not necessarily together) is
(a) 210
(b) 5040
(c) 6×⁷C₃
(d) ⁷P₃   

Question: Two players P₁ and P₂ plays a series of 2n games.
Each game can result in either a win or loss for P₁.Total number of ways in which P₁can win the series of these games, is equal to

Question: Total number of ways of giving at least one coin out of three 25 paisa and two 50 paisa coins to a beggar is
(a) 32A
(b) 12
(c) 11
(d) ¹²P₁ − 1 

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

Question. How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent ? 
(a) 7 . ⁶C₄ . ⁸C₄
(b) 8 . ⁶C₄ . ⁷C₄
(c) 6 . 7 . ⁸C₄
(d) 6 . 8 . ⁷C₄

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 to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote, is
(a) 6210
(b) 385
(c) 1110
(d) 5040

Question. If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number
(a) 602
(b) 603
(c) 600
(d) 601

Question. It is required to seat 5 men and 4 women in a row, so that the women occupy the even places. The number of such arrangement equals.
(a) 1440
(b) 2800
(c) 2880
(d) 2840

Question. The number of ways that two different rings can be worn in four fingers with atmost one in each finger, is
(a) 8
(b) 10
(c) 11
(d) 12

Question. The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time, is
(a) 432
(b) 108
(c) 36
(d) 18

Question. The number of numbers between 400 and 1000 that can be made with the digits 2, 3, 4, 5, 6 and 0, when repetition of digits is not allowed, is
(a) 40
(b) 50
(c) 60
(d) 70

Question. The number of 4 letter words that can be formed from alphabets of the word ‘PART’, when repetition is allowed, is
(a) 24
(b) 196
(c) 1
(d) 256

Question. The number of six-digit numbers all digits of which are odd, is ……… .
(a) 53
(b) 54
(c) 55
(d) 56

Question. The number of 5-digit telephone numbers having atleast one of their digits repeated is
(a) 90000
(b) 10000
(c) 30240
(d) 69760

Question. Find the number of permutations of the letters of the word ‘INDEPENDENCE’ is
(a) 1663400
(b) 1663300
(c) 1663200
(d) 1663100

Question. If the ratio ²ⁿC₃ : ⁿC₃ is equal to 11 : 1, the value of n is
(a) 4
(b) 5
(c) 6
(d) 7

Question. ¹⁵C₅ + ¹⁵C₉ – ¹⁵C₆ – ¹⁵C₇ is equal to ……… .
(a) 0
(b) 2
(c) 1
(d) 3

Question. If ⁿP_r = 840 and ⁿC_r = 35, then r is equal to ……… .
(a) 4!
(b) 3!
(c) 4
(d) 3

Question. Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done, if atleast 2 are red, is
(a) 70
(b) 75
(c) 78
(d) 80

Question. The number of words in which the twoC are together but no two S are together, is
(a) 120
(b) 96
(c) 24
(d) 420

Question. The number of words in which the consonants appear in alphabetic order is
(a) 42
(b) 40
(c) 420
(d) 280

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

Question. The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is
(a) ¹⁶C₁₁
(b) ¹⁶C₅
(c) ¹⁶C₉
(d) ²⁰C₉

Question. The number of ways in which we can choose a committee from four men and six women, so that the committee includes atleast two men and exactly twice as many women as men is
(a) 94
(b) 126
(c) 128
(d) None of these

Question. The number of diagonals of n-sided polygon is
(a) ⁿC₂ + n
(b) ⁿC₂ – n
(c) n x ^nC₂
(d) ⁿC₂ − 2n

Case Based MCQs

Five students Ajay, Shyam, Yojana, Rahul and Akansha are sitting in a play ground in a line.

Based on the above information, answer the following questions.

Question. Total number of ways of sitting arrangement of five students is
(a) 120
(b) 60
(c) 24
(d) None of these

Question. Total number of arrangement of sitting, if Ajay and Yojana sit together, is
(a) 60
(b) 48
(c) 72
(d) 120

Question. Total number of arrangement ‘Yojana and Rahul sitting at extreme position’ is
(a) 24
(b) 36
(c) 48
(d) 12

Question. Total number of arrangement, if shyam is sitting in the middle, is
(a) 24
(b) 12
(c) 6
(d) 36

Question. Total number of arrangement sitting Yojana and Rahul not sit together, is
(a) 72
(b) 120
(c) 60
(d) 144

Republic day is a national holiday of India. It honours the date on which the constitution of India came into effect on 26 January 1950 replacing the Government of India Act (1935) as the governing document of India and thus, turning the nation into a newly formed republic.
Answer the following question, which are based on the word “REPUBLIC”.

Question. Find the number of arrangements of the letters of the word ‘REPUBLIC’.
(a) 40300
(b) 30420
(c) 40320
(d) 40400

Question. How many arrangements start with a vowel?
(a) 12015
(b) 15120
(a) 12018
(d) 15100

Question. Which concept is used for finding the arrangements start with a vowel?
(a) Permutation
(b) FPM
(c) Combination
(d) FPA

Question. If the number of arrangements of the letters of the word ‘REPUBLIC’ is abcde, the (a + b + c + d + e) is
(a) 10
(b) 9
(c) 8
(d) 15

Question. If the number of arrangements start with a vowel is abcde, then (a + b) − (d + e) is
(a) 2
(b) 3
(c) 4
(d) 5