Class 11 Mathematics Chapter 7 Permutations and Combinations MCQ Questions with Answer

Permutations and Combinations Class 11 MCQ is one of the best strategies to prepare for the CBSE Class 11 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more Permutations and Combinations class 11 MCQ which will help them all through their board test.

Permutations and Combinations Class 11 MCQ Questions with Answer

Class 11 Math MCQ with answers are given here to Chapter 7 Permutations and Combinations. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 11 Mathematics syllabus. By Solving these Class 11 MCQs, you will be able to analyze all of the concepts quickly in the Chapter and get ready for the Class 11 Annual exam.

Learn Permutations and Combinations Class 11 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 11 Permutations and Combinations MCQ with answers given below.

Question 1. 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

Question 2. 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

Question 3. 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

Question 4. Total number of divisors of 5880 is equal to
(a) 48
(b) 24
(c) 96
(d) 16

Question 5. 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 these

Question 6. 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

Question 7. 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 crepresents the number of permutation of (x – 11)things taken together so that a = 182bc, then x is equal to
(a) 15
(b) 12
(c) 10
(d) 18

Question 8. 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– 4⁵

Question 9. The value of (⁷C₀ + ⁷C₁) +(⁷C₁ + ⁷C₂) +….+(⁷C₆ + ⁷C₇) is
(a) 2⁷ – 1 
(b) 2⁸ – 2
(c) 2⁸ – 1 
(d) 2⁸

Question 10. The number of non-negative integral solutions of x + y + z ≤ n, where n ÎNis
(a) ^{n + 3}C
(b) ^{n + 4}C
(c) ^{n + 5}C
(d) ^{n + 2}C

Question 11. 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

Question 12. 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

Question 13. Find the number of different words that can be formed from the letters of the word TRIANGLE, so that no vowels are together. 
(a) 14000
(b) 14500
(c) 14400
(d) 14402

Question 14. The number of different four digit numbers that can be formed with the digits 2, 3, 4, 7 and using each digit only once is 
(a) 120
(b) 96
(c) 24
(d) 100

Question 15. 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

Question 16. The number of 5-digits telephone numbers having atleast one of their digits repeated, is 
(a) 90000
(b) 100000
(c) 30240
(d) 69760

Question 17. We are to form different words with the letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then m m 1 2 / is equal to
(a) 30
(b) 60
(c) 90
(d) 180

Question 18. 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

Question 19. 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

Question 20. 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 these

Question 21. 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

Question 22. 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 number 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

Question 23. 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 these

Question 24. The products of any r consecutive natural numbers is always divisible by
(a) r!
(b) r²
(c) rⁿ
(d) None of these

Question 25. The value of 2π[1.3.5….. K(2n – 3) (2n – 1)] is
(a) (2n)|/n!
(b) (2n)!/2ⁿ
(c) n)!/(2n)!
(d) None of these

Whoever needs to take the CBSE Class 11 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 11 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Permutations and Combinations Class 11 MCQ are ready by the subject specialists themselves.

Question 26. 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

Question 27. If 2n + 1P^n-1:2^n-1 Pn = 3;5, then the value of n is equal to
(a) 4
(b) 3
(c) 2
(d) 1

Question 28. How many even numbers of 3 different digits can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition of digits is not allowed)?
(a) 224
(b) 280
(c) 324
(d) None of these

Question 29. The total number of 9-digit numbers which have all different digits is [NCERT Exemplar]
(a) 10!
(b) 9!
(c) 9 x 9!
(d) 10 x 10!

Question 30. The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is 
(a) 1440
(b) 144
(c) 7!
(d) ⁴C₄ x ³C₃

Question 31. The exponent of 3 in 100! is
(a) 47
(b) 48
(c) 49
(d) 50

Question 32. If ⁵Pr =2⁶P_r-1 , then the value of r is 
(a) 10
(b) 3
(c) 0
(d) None of these

Question 33. In how many ways can the letters of the word PERMUTATIONS be arranged, if the words start with P and end with S? 
(a) 1814400
(b) 1814405
(c) 1824050
(d) None of these

Question 34. How many different non-digit numbers can be formed from the digits of the number 223355888 by rearrangement of the digits so that the odd digits occupy even places?
(a) 16
(b) 36
(c) 60
(d) 180

Question 35. 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 these

Question 36. 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 these

Question 37. If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
(a) 324
(b) 341
(c) 359
(d) None of these

Question 38. Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs.Find the total number of possible arrangements.
(a) 1440
(b) 1450
(c) 1460
(d) None of these

Question 39. If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary. Then, what is the rank of the word RACHIT? 
(a) 479
(b) 480
(c) 481
(d) 482

Question 40. 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 41. ⁿC_r + 2ⁿC_r-1 + 2 ⁿC_r-2 is equal to
(a) ⁿ⁺¹C_r 
(b) ⁿ⁺¹C_r+1
(c) ⁿ⁺²C_r
(d) ⁿ⁺²C_r+1,

Question 42. If ⁿC₃ + ⁿC₄ > n+¹C₃ ,then
(a) n > 6
(b) n > 7
(c) n < 6
(d) None of these

Question 43. If a denotes the number of permutations of x + 2 things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x – 11 things taken all at a time such that a = 182 bc, then the value of x is
(a) 15
(b) 12
(c) 10
(d) 18

Question 44. If the letters of the word MOTHER are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MOTHERis
(a) 240
(b) 261
(c) 308
(d) 309

Question 45. In a circus there are ten cages for accommodating ten animals. Out of these four cages are so small that five out of 10 animals cannot enter into them. In how many ways will it be possible to accommodate ten animals in these ten cages?
(a) 66400
(b) 86400
(c) 96400
(d) None of these

Question 46. The total number of permutations of n (> 1) different things taken not more than r at a time, when each thing may be repeated any number of times is
(a) n(nⁿ-1)/n-1
(b) n(nⁿ-1)/n-1
(c) n(nⁿ-1)/n-1
(d) None of these

Question 47. The number of ways in which seven persons can be arranged at a round table, if two particular persons may not sit together is
(a) 480
(b) 120
(c) 80
(d) None of these

Question 48. In how many ways can 15 members of a council sit along a circular table, when the Secretary is to sit on one side of the Chairman and the Deputy Secretary on the other side?
(a) 2 x 12!
(b) 24
(c) 2 x 15!
(d) None of these

Question 49. Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together. [NCERT Exemplar]
(a) ^{n- 3}C_r-3(r-2)!3!
(b) ^{n- 3}C_r-3(r-3)!3!
(c) ^{n- 3}C_r-3(r-2)!3!
(d) None of these

Question 50. There are 10 persons named P₁ , P₂ , P₃ . . . , . P₁₀ Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements. 
(a) 4210
(b) 4200
(c) 4203
(d) 4205

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