Students can refer to the following Linear Permutations and Combinations MCQ Questions for Class 11 Maths with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple choice questions for Linear Permutations and Combinations Class 11 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

**Linear Permutations and Combinations MCQ Questions for Class 11 Maths with Answers**

We have provided below Linear Permutations and Combinations MCQ Questions for Class 11 Maths with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Linear Permutations and Combinations MCQs in Class 11 Mathematics pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

**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 these

## Answer

C

**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. 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

## Answer

B

**Question. There are 4 parcels and 5 post offices. In how many ways can 4 parcels be got registered?**

(a) 20

(b) 4^{5}

(c) 5^{4}

(d) 5^{4}– 4^{5}

## Answer

C

**Question. The value of ( ^{7}C_{0} + ^{7}C_{1}) +(^{7}C_{1} + ^{7}C_{2}) +….+(^{7}C_{6} + ^{7}C_{7}) is**

(a) 2

^{7}– 1

(b) 2

^{8}– 2

(c) 2

^{8}– 1

(d) 2

^{8}

## Answer

B

**Question. The number of products that can be formed with 10 prime numbers taken two or more at a time is**

(a) 2^{10}

(b) 2^{10} – 1

(c) 2^{10} – 11

(d) 2^{10} – 10

## 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) ^{37}C_{6} (d) 38

## Answer

A

**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. Total number of divisors of 5880 is equal to**

(a) 48

(b) 24

(c) 96

(d) 16

## 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. 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

## Answer

C

**Question. 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

## Answer

C

**Question. 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

## 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. 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. 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. 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

## Answer

A

**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. 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. The number of 5-digits telephone numbers having atleast one of their digits repeated, is **

(a) 90000

(b) 100000

(c) 30240

(d) 69760

## Answer

D

**Question. 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

## Answer

A

**Question. The value of 2π[1.3.5….. K(2n – 3) (2n – 1)] is**

(a) (2n)|/n!

(b) (2n)!/2^{n}

(c) n)!/(2n)!

(d) None of these

## 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. 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

## Answer

A

**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 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

## Answer

D

**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 these

## Answer

C

**Question. The products of any r consecutive natural numbers is always divisible by**

(a) r!

(b) r^{2}

(c) r^{n}

(d) None of these

## Answer

A

**Question. The exponent of 3 in 100! is**

(a) 47

(b) 48

(c) 49

(d) 50

## Answer

C

**Question. If ^{5}Pr =2^{6}P_{r-1} , then the value of r is **

(a) 10

(b) 3

(c) 0

(d) None of these

## Answer

B

**Question. 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

## Answer

A

**Question. 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

## Answer

C

**Question. 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

## Answer

A

**Question. 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!

## Answer

C

**Question. 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) ^{4}C_{4} x ^{3}C_{3}

## Answer

B

**Question. 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

## Answer

A

**Question. 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

## Answer

C

**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

## Answer

B

**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 these

## Answer

A

**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) ^{7}P_{4}

(b) 7^{4}

(c) 7^{4} – ^{7}P_{4}

(d) None of these

## Answer

C

**Question. 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

## Answer

A

**Question. 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

## Answer

D

**Question. 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

## Answer

A

**Question. There are 10 persons named P _{1} , P_{2} , P_{3} . . . , . P_{10} 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

## Answer

B

**Question. ^{n}C_{r} + 2^{n}C_{r-1} + 2 ^{n}C_{r-2} is equal to**

(a)

^{n+1}C

_{r}

(b)

^{n+1}C

_{r+1}

(c)

^{n+2}C

_{r}(d)

^{n+2}C

_{r+1},

## Answer

C

**Question. If ^{n}C_{3} + ^{n}C_{4} > n+^{1}C_{3} ,then**

(a) n > 6

(b) n > 7

(c) n < 6

(d) None of these

## Answer

A

**Question. 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

## Answer

B

**Question. 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

## Answer

B

**Question. 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(n^{n}-1)/n-1

(b) n(n^{n}-1)/n-1

(c) n(n^{n}-1)/n-1

(d) None of these

## Answer

C

**Question. 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

## Answer

A

**Question. 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

## Answer

A

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