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RD Sharma solutions for Class 11 Mathematics chapter 16 - Permutations

Mathematics Class 11

RD Sharma Mathematics Class 11 Chapter 16: Permutations

Ex. 16.10Ex. 16.20Ex. 16.30Ex. 16.40Ex. 16.50Others

Chapter 16: Permutations Exercise 16.10 solutions [Pages 4 - 5]

Ex. 16.10 | Q 1.1 | Page 4

Compute:

(i)$\frac{30!}{28!}$

Ex. 16.10 | Q 1.2 | Page 4

Compute:

$\frac{11! - 10!}{9!}$
Ex. 16.10 | Q 1.3 | Page 4

Compute:

L.C.M. (6!, 7!, 8!)

Ex. 16.10 | Q 2 | Page 4

Prove that

$\frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!} = \frac{122}{11!}$
Ex. 16.10 | Q 3.1 | Page 4

Find x in each of the following:

$\frac{1}{4!} + \frac{1}{5!} = \frac{x}{6!}$
Ex. 16.10 | Q 3.2 | Page 4

Find x in each of the following:

$\frac{x}{10!} = \frac{1}{8!} + \frac{1}{9!}$
Ex. 16.10 | Q 3.3 | Page 4

Find x in each of the following:

$\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}$
Ex. 16.10 | Q 4.1 | Page 4

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10

Ex. 16.10 | Q 4.2 | Page 4

Convert the following products into factorials:

3 · 6 · 9 · 12 · 15 · 18

Ex. 16.10 | Q 4.3 | Page 4

Convert the following products into factorials:

(n + 1) (n + 2) (n + 3) ... (2n)

Ex. 16.10 | Q 4.4 | Page 4

Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)

Ex. 16.10 | Q 5.1 | Page 4

Which of the following are true:

(2 +3)! = 2! + 3!

Ex. 16.10 | Q 5.2 | Page 4

Which of the following are true:

(2 × 3)! = 2! × 3!

Ex. 16.10 | Q 6 | Page 4

Prove that: n! (n + 2) = n! + (n + 1)!

Ex. 16.10 | Q 7 | Page 4

If (n + 2)! = 60 [(n − 1)!], find n.

Ex. 16.10 | Q 8 | Page 4

If (n + 1)! = 90 [(n − 1)!], find n.

Ex. 16.10 | Q 9 | Page 4

If (n + 3)! = 56 [(n + 1)!], find n.

Ex. 16.10 | Q 10 | Page 5

If $\frac{(2n)!}{3! (2n - 3)!}$  and $\frac{n!}{2! (n - 2)!}$  are in the ratio 44 : 3, find n.

Ex. 16.10 | Q 11.1 | Page 5

Prove that:

$\frac{n!}{(n - r)!}$ = n (n − 1) (n − 2) ... (n − (r − 1))
Ex. 16.10 | Q 11.2 | Page 5

Prove that:

$\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}$

Ex. 16.10 | Q 12 | Page 5

Prove that:

$\frac{(2n + 1)!}{n!}$ = 2n [1 · 3 · 5 ... (2n − 1) (2n + 1)]

Chapter 16: Permutations Exercise 16.20 solutions [Pages 14 - 16]

Ex. 16.20 | Q 1 | Page 14

In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?

Ex. 16.20 | Q 2 | Page 14

A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?

Ex. 16.20 | Q 3 | Page 14

From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?

Ex. 16.20 | Q 4 | Page 14

A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?

Ex. 16.20 | Q 5 | Page 14

There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?

Ex. 16.20 | Q 6 | Page 15

A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?

Ex. 16.20 | Q 7 | Page 15

In how many ways can an examinee answer a set of ten true/false type questions?

Ex. 16.20 | Q 8 | Page 15

A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?

Ex. 16.20 | Q 9 | Page 15

There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?

Ex. 16.20 | Q 10 | Page 15

There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?

Ex. 16.20 | Q 11 | Page 15

Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?

Ex. 16.20 | Q 12 | Page 15

A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?

Ex. 16.20 | Q 13 | Page 15

Twelve students complete in a race. In how many ways first three prizes be given?

Ex. 16.20 | Q 14 | Page 15

How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?

Ex. 16.20 | Q 15 | Page 15

From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?

Ex. 16.20 | Q 16 | Page 15

How many three-digit numbers are there with no digit repeated?

Ex. 16.20 | Q 17 | Page 15

How many three-digit numbers are there?

Ex. 16.20 | Q 18 | Page 15

How many three-digit odd numbers are there?

Ex. 16.20 | Q 19.1 | Page 15

How many different five-digit number licence plates can be made if

first digit cannot be zero and the repetition of digits is not allowed,

Ex. 16.20 | Q 19.2 | Page 15

How many different five-digit number licence plates can be made if

the first-digit cannot be zero, but the repetition of digits is allowed?

Ex. 16.20 | Q 20 | Page 15

How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?

Ex. 16.20 | Q 21 | Page 15

Since the  number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = 2xx4xx3xx2=48

Ex. 16.20 | Q 22 | Page 15

In how many ways can six persons be seated in a row?

Ex. 16.20 | Q 23 | Page 15

How many 9-digit numbers of different digits can be formed?

Ex. 16.20 | Q 24 | Page 15

How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?

Ex. 16.20 | Q 25 | Page 15

How many 3-digit numbers are there, with distinct digits, with each digit odd?

Ex. 16.20 | Q 26 | Page 15

How many different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?

Ex. 16.20 | Q 27 | Page 15

How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?

Ex. 16.20 | Q 28 | Page 15

How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?

Ex. 16.20 | Q 29 | Page 15

Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?

Ex. 16.20 | Q 30 | Page 16

A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.

Ex. 16.20 | Q 31 | Page 16

A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.

Ex. 16.20 | Q 32 | Page 16

In how many ways can three jobs I, II and III be assigned to three persons AB and C if one person is assigned only one job and all are capable of doing each job?

Ex. 16.20 | Q 33 | Page 16

How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?

Ex. 16.20 | Q 34 | Page 16

How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?

Ex. 16.20 | Q 35 | Page 16

If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?

Ex. 16.20 | Q 36 | Page 16

A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?

Ex. 16.20 | Q 37 | Page 16

How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?

Ex. 16.20 | Q 38 | Page 16

How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?

Ex. 16.20 | Q 39 | Page 16

How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?

Ex. 16.20 | Q 40 | Page 16

How many five 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?

Ex. 16.20 | Q 41 | Page 16

Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.

Ex. 16.20 | Q 42 | Page 16

Find the number of ways in which one can post 5 letters in 7 letter boxes ?

Ex. 16.20 | Q 43 | Page 16

Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?

Ex. 16.20 | Q 44 | Page 16

Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?

Ex. 16.20 | Q 45 | Page 16

In how many ways can 5 different balls be distributed among three boxes?

Ex. 16.20 | Q 46 | Page 16

In how many ways can 7 letters be posted in 4 letter boxes?

Ex. 16.20 | Q 47 | Page 16

In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?

Ex. 16.20 | Q 48 | Page 16

There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?

Chapter 16: Permutations Exercise 16.30 solutions [Pages 28 - 29]

Ex. 16.30 | Q 1.1 | Page 28

Evaluate each of the following:

8P3

Ex. 16.30 | Q 1.2 | Page 28

Evaluate each of the following:

10P
Ex. 16.30 | Q 1.3 | Page 28

Evaluate each of the following:

6P

Ex. 16.30 | Q 1.4 | Page 28

Evaluate each of the following:

P(6, 4)

Ex. 16.30 | Q 2 | Page 28

If P (5, r) = P (6, r − 1), find r ?

Ex. 16.30 | Q 3 | Page 28

If 5 P(4, n) = 6. P (5, n − 1), find n ?

Ex. 16.30 | Q 4 | Page 28

If P (n, 5) = 20. P(n, 3), find n ?

Ex. 16.30 | Q 5 | Page 28

If nP4 = 360, find the value of n.

Ex. 16.30 | Q 6 | Page 28

If P (9, r) = 3024, find r.

Ex. 16.30 | Q 7 | Page 28

If P(11, r) = P (12, r − 1) find r.

Ex. 16.30 | Q 8 | Page 28

If P (n, 4) = 12 . P (n, 2), find n.

Ex. 16.30 | Q 9 | Page 28

If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.

Ex. 16.30 | Q 10 | Page 28

If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.

Ex. 16.30 | Q 11 | Page 28

If P (n, 5) : P (n, 3) = 2 : 1, find n.

Ex. 16.30 | Q 12 | Page 28

Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (nn) = P (n + 1, n + 1) − 1.

Ex. 16.30 | Q 13 | Page 28

If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.

Ex. 16.30 | Q 14 | Page 28

If n +5Pn +1 =$\frac{11 (n - 1)}{2}$n +3Pn, find n.

Ex. 16.30 | Q 15 | Page 28

In how many ways can five children stand in a queue?

Ex. 16.30 | Q 16 | Page 28

From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?

Ex. 16.30 | Q 17 | Page 28

Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?

Ex. 16.30 | Q 18 | Page 28

Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?

Ex. 16.30 | Q 19 | Page 28

Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.

Ex. 16.30 | Q 20 | Page 28

How many three-digit numbers are there, with distinct digits, with each digit odd?

Ex. 16.30 | Q 21 | Page 28

How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?

Ex. 16.30 | Q 22 | Page 28

How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?

Ex. 16.30 | Q 23 | Page 29

There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?

Ex. 16.30 | Q 24 | Page 29

There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?

Ex. 16.30 | Q 25 | Page 29

How many three-digit numbers are there, with no digit repeated?

Ex. 16.30 | Q 26 | Page 29

How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?

Ex. 16.30 | Q 27 | Page 29

In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?

Ex. 16.30 | Q 28 | Page 29

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, find the value of x.

Ex. 16.30 | Q 29 | Page 29

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

Ex. 16.30 | Q 30 | Page 29

How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?

Ex. 16.30 | Q 31 | Page 29

Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, if no digit is repeated? How many of these will be even?

Ex. 16.30 | Q 32 | Page 29

All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.

Chapter 16: Permutations Exercise 16.40 solutions [Pages 36 - 37]

Ex. 16.40 | Q 1 | Page 36

In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?

Ex. 16.40 | Q 2.1 | Page 36

In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels come together?

Ex. 16.40 | Q 2.2 | Page 36

In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels never come together?

Ex. 16.40 | Q 2.3 | Page 36

In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels occupy only the odd places?

Ex. 16.40 | Q 3 | Page 36

How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?

Ex. 16.40 | Q 4 | Page 37

How many words can be formed out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?

Ex. 16.40 | Q 5 | Page 37

How many different words can be formed with the letters of word 'SUNDAY'? How many of the words begin with N? How many begin with N and end in Y?

Ex. 16.40 | Q 6.1 | Page 37

How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the vowels are always together?

Ex. 16.40 | Q 6.2 | Page 37

How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the letter G always occupies the first place?

Ex. 16.40 | Q 6.3 | Page 37

How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the letters P and I respectively occupy first and last place?

Ex. 16.40 | Q 6.4 | Page 37

How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the vowels always occupy even places?

Ex. 16.40 | Q 7.1 | Page 37

How many permutations can be formed by the letters of the word, 'VOWELS', when

there is no restriction on letters?

Ex. 16.40 | Q 7.2 | Page 37

How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?

Ex. 16.40 | Q 7.3 | Page 37

How many permutations can be formed by the letters of the word, 'VOWELS', when

each word begins with O and ends with L?

Ex. 16.40 | Q 7.4 | Page 37

How many permutations can be formed by the letters of the word, 'VOWELS', when

all vowels come together?

Ex. 16.40 | Q 7.5 | Page 37

How many permutations can be formed by the letters of the word, 'VOWELS', when

all consonants come together?

Ex. 16.40 | Q 8 | Page 37

How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?

Ex. 16.40 | Q 9 | Page 37

In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?

Ex. 16.40 | Q 10 | Page 37

m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as$\frac{m! (m + 1)!}{(m - n + 1) !}$

Ex. 16.40 | Q 11.1 | Page 37

How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if

4 letters are used at a time?

Ex. 16.40 | Q 11.2 | Page 37

How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if
all letters are used at a time.

Ex. 16.40 | Q 11.3 | Page 37

How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if

all letters are used but first is vowel.

Ex. 16.40 | Q 12 | Page 37

How many three letter words can be made using the letters of the word 'ORIENTAL'?

Chapter 16: Permutations Exercise 16.50 solutions [Pages 42 - 44]

Ex. 16.50 | Q 1.1 | Page 42

Find the number of words formed by permuting all the letters of the following words:
INDEPENDENCE

Ex. 16.50 | Q 1.2 | Page 42

Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE

Ex. 16.50 | Q 1.3 | Page 42

Find the number of words formed by permuting all the letters of the following words:
ARRANGE

Ex. 16.50 | Q 1.4 | Page 42

Find the number of words formed by permuting all the letters of the following words:

INDIA

Ex. 16.50 | Q 1.5 | Page 42

Find the number of words formed by permuting all the letters of the following words:

PAKISTAN

Ex. 16.50 | Q 1.6 | Page 42

Find the number of words formed by permuting all the letters of the following words:

RUSSIA

Ex. 16.50 | Q 1.7 | Page 42

Find the number of words formed by permuting all the letters of the following words:
SERIES

Ex. 16.50 | Q 1.8 | Page 42

Find the number of words formed by permuting all the letters of the following words:
EXERCISES

Ex. 16.50 | Q 1.9 | Page 42

Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE

Ex. 16.50 | Q 2 | Page 42

In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?

Ex. 16.50 | Q 3 | Page 42

How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?

Ex. 16.50 | Q 4 | Page 42

Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.

Ex. 16.50 | Q 5 | Page 43

How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?

Ex. 16.50 | Q 6 | Page 43

How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?

Ex. 16.50 | Q 7 | Page 43

How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?

Ex. 16.50 | Q 8 | Page 43

How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?

Ex. 16.50 | Q 9 | Page 43

How many number of four digits can be formed with the digits 1, 3, 3, 0?

Ex. 16.50 | Q 10 | Page 43

In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?

Ex. 16.50 | Q 11 | Page 43

How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.

Ex. 16.50 | Q 12 | Page 43

How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?

Ex. 16.50 | Q 13 | Page 43

How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?

Ex. 16.50 | Q 14 | Page 43

Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.

Ex. 16.50 | Q 15 | Page 43

There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?

Ex. 16.50 | Q 16 | Page 43

How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?

Ex. 16.50 | Q 17 | Page 43

A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?

Ex. 16.50 | Q 18 | Page 43

In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?

Ex. 16.50 | Q 19 | Page 43

How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?

Ex. 16.50 | Q 20 | Page 43

In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?

Ex. 16.50 | Q 21 | Page 43

Find the total number of permutations of the letters of the word 'INSTITUTE'.

Ex. 16.50 | Q 22 | Page 43

The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.

Ex. 16.50 | Q 23 | Page 43

If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.

Ex. 16.50 | Q 24 | Page 43

If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.

Ex. 16.50 | Q 25 | Page 43

If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?

Ex. 16.50 | Q 26 | Page 43

Find the total number of ways in which six '+' and four '−' signs can be arranged in a line such that no two '−' signs occur together.

Ex. 16.50 | Q 27.1 | Page 44

In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?

Ex. 16.50 | Q 27.2 | Page 44

In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:

the relative order of vowels and consonants do not alter?

Ex. 16.50 | Q 28 | Page 44

The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?

Chapter 16: Permutations solutions [Page 45]

Q 1 | Page 45

In how many ways can 4 letters be posted in 5 letter boxes?

Q 2 | Page 45

Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?

Q 3 | Page 45

In how many ways 4 women draw water from 4 taps, if no tap remains unused?

Q 4 | Page 45

Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.

Q 5 | Page 45

Write the number of arrangements of the letters of the word BANANA in which two N's come together.

Q 6 | Page 45

Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?

Q 7 | Page 45

Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?

Q 8 | Page 45

Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.

Q 9 | Page 45

Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?

Q 10 | Page 45

Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?

Q 11 | Page 45

Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?

Q 12 | Page 45

Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?

Chapter 16: Permutations solutions [Pages 46 - 47]

Q 1 | Page 46

The number of permutations of n different things taking r at a time when 3 particular things are to be included is

• n − 3Pr − 3

•  n − 3Pr

• nPr − 3

• r ! n − 3Cr − 3

Q 2 | Page 46

The number of five-digit telephone numbers having at least one of their digits repeated is

• 90000

• 100000

• 30240

• 69760

Q 3 | Page 46

The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is

• 574

• 36

• 754

• 144

Q 4 | Page 46

How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?

• 420

• 360

• 400

• 300

Q 5 | Page 46

The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is

• 1958

• 1956

• 16

• 64

Q 6 | Page 46

The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is

• 360

• 240

• 120

• none of these.

Q 7 | Page 46

The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is

• 12

• 24

• 18

• none of these.

Q 8 | Page 46

The number of arrangements of the word "DELHI" in which E precedes I is

• 30

• 60

• 120

• 59

Q 9 | Page 46

The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is

• 360

• 256

• 444

• none of these.

Q 10 | Page 46

The number of ways to arrange the letters of the word CHEESE are

• 120

• 240

• 720

• 6

Q 11 | Page 46

Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is

• 24

• 30

• 125

• 100

Q 12 | Page 46

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

• 324

• 341

• 359

• none of these

Q 13 | Page 46

If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is

• 10

• 8

• 6

• none of these.

Q 14 | Page 47

The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is

• 4! × 3!

• 4!

• 3! × 3!

• none of these.

Q 15 | Page 47

A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

• 216

• 600

• 240

• 3125

Q 16 | Page 47

The product of r consecutive positive integers is divisible by

• r !

• (r − 1) !

• (r + 1) !

• none of these.

Q 17 | Page 47

If k + 5Pk + 1 =$\frac{11 (k - 1)}{2}$. k + 3Pk , then the values of k are

• 7 and 11

• 6 and 7

• 2 and 11

• 2 and 6

Q 18 | Page 47

The number of arrangements of the letters of the word BHARAT taking 3 at a time is

• 72

• 120

• 14

• none of these.

Q 19 | Page 47

The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is

• 18

• 35

• 36

• none of these

Q 20 | Page 47

The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is

•  60 × 5!

• 15 × 4! × 5!

• 4! × 5!

• none of these.

Q 21 | Page 47

The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is

• 576

• 4C3 × 4!

• 2 × 4!

• none of these.

Q 22 | Page 47

In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is

• 122 − 1

• 212

• 212 − 1

• none of these

Chapter 16: Permutations

Ex. 16.10Ex. 16.20Ex. 16.30Ex. 16.40Ex. 16.50Others

RD Sharma Mathematics Class 11 RD Sharma solutions for Class 11 Mathematics chapter 16 - Permutations

RD Sharma solutions for Class 11 Maths chapter 16 (Permutations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Class 11 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics chapter 16 Permutations are Concept of Combinations, Fundamental Principle of Counting, Concept of Permutations, Introduction of Permutations and Combinations, Permutation Formula to Rescue and Type of Permutation, Smaller Set from Bigger Set, Derivation of Formulae and Their Connections, Simple Applications of Permutations and Combinations, Factorial N (N!) Permutations and Combinations.

Using RD Sharma Class 11 solutions Permutations exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer RD Sharma Textbook Solutions to score more in exam.

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