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RD Sharma Solution Class 11 Mathematics Chapter 16 Permutations

Chapter 16 – Permutations Exercise Ex. 16.1

Question 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 2
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 2
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 3

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 3

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 11
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 11
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 13
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 13
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 14
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 14
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 15
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 15
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 16
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 16
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 17
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 17
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 18
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 18
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Chapter 16 – Permutations Exercise Ex. 16.2

Question 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 2
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 2
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 3
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 3
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 4
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 4
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 11
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 11
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 13
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 13
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 14
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 14
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 15
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 15
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 16
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 16
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 17

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

Solution 17

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 18
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 18
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 19
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 19
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 20
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 20
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 21
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 21
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 22
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 22
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 23
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 23
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 24
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 24
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 25
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 25
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 26
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?
Solution 26

Any number less than 1000 may be any of a number from one-digit number, two-digit number and three-digit number.

One-digit odd number:

3 possible ways are there. These numbers are 3 or 5 or 7.

Two-digit odd number:

Tens place can be filled up by 3 ways (using any of the digit among 3, 5 and 7) and then the ones place can be filled in any of the remaining 2 digits.

So, there are 3 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 2 = 6 such 2-digit numbers.

Three-digit odd number:

Ignore the presence of zero at ones place for some instance.

Hundreds place can be filled up in 3 ways (using any of any of the digit among 3, 5 and 7), then tens place in 3 ways by using remaining 3 digits (after using a digit, there will be three digits) and then the ones place in 2 ways.

So, there are a total of 3 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 3 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 2 = 18 numbers of 3-digit numbers which includes both odd and even numbers (ones place digit are zero). In order to get the odd numbers, it is required to ignore the even numbers i.e. numbers ending with zero.

To obtain the even 3-digit numbers, ones place can be filled up in 1 way (only 0 to be filled), hundreds place in 3 ways (using any of the digit among 3, 5, 7) and then tens place in 2 ways (using remaining 2 digits after filling up hundreds place).

So, there are a total of 1 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 3 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 2 = 6 even 3-digit numbers using the digits 0, 3, 5 and 7 (repetition not allowed)

So, number of three-digit odd numbers using the digits 0, 3, 5 and 7 (repetition not allowed) = 18 –  6 = 12.

Therefore, odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed are 3 + 6 + 12 = 21.

Question 27
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 27
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 28
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 28
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 29
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 29
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 30
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 30
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 31

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 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?

Solution 31

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 32
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 32
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 33
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 33
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 34
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 34
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 35

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

Solution 35

The given digits are 1, 2, 3 and 4. These digits can be repeated while forming the numbers. So, number of required four digit natural numbers can be found as follows.

Consider four digit natural numbers whose digit at thousandths place is 1.

Here, hundredths place can be filled in 4 ways. (Using the digits 1 or 2 or 3 or 4)

Similarly, tens place can be filled in 4 ways. (Using the digits 1 or 2 or 3 or 4)

Ones place can be filled in 4 ways. (Using the digits 1 or 2 or 3 or 4)

Number of four digit natural numbers whose digit at thousandths place is 1 = 4 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 4 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 4 = 64

Similarly, number of four digit natural numbers whose digit at thousandths place is 2 = 4 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 4 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 4  = 64

Now, consider four digit natural numbers whose digit at thousandths place is 4:

Here, if the digit at hundredths place is 1, then tens place can be filled in 4 ways and ones place can also be filled in 4 ways.

If the digit at hundredths place is 2, then tens place can be filled in 4 ways and ones place can also be filled in 4 ways.

If the digit at hundredths place is 3 and the digit at tens place is 1, then ones place can be filled in 4 ways.

If the digit at hundredths place is 3 and the digit at tens place is 2, then ones place can be filled only in 1 way so that the number formed is not exceeding 4321.

Number of four digit natural numbers not exceeding 4321 and digit at thousandths place is 3 = 4 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 4 + 4 Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations 4 + 4 + 1 = 37

Thus, required number of four digit natural numbers not exceeding 4321 is 64 + 64 + 64 + 37 = 229.

Question 36

How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7, and 9 when on digit is repeated? How many of them are divisible by 10?

Solution 36

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 37
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 37
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 38
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 38
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 39

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 39

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 40

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 40

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 41

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 41

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 42

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 42

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 43

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 43

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 44

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 44

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 45

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 45

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 46

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 46

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 47

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 47

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 48

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

Solution 48

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 49

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 49

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 50

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 50

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 51

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 51

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 52

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.

Solution 52

 

Each lamps has two possibilities either it can be switched on or off.

There are 10 lamps in the hall.

So the total numbers of possibilities are 210.

To illuminate the hall we require at least one lamp is to be switched on.

There is one possibility when all the lamps are switched off. If all the bulbs are switched off then hall will not be illuminated.

So the number of ways in which the hall can be illuminated is 210-1.

Chapter 16 – Permutations Exercise Ex. 16.3

Question 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 2
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 2
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 3
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 3
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 4
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 4
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 5
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 5
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 11
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 11
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 13
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 13
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 14
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 14
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 15
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 15
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 16
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 16
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 17
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 17
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 18
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 18
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 19
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 19
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 20
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 20
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 21
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 21
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 22
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 22
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 23
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 23
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 24
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 24
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 25
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 25
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 26
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 26
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 27
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 27
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 28
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 28
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 29
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 29
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 30
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 30
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 31
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 31
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 32
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 32
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 33
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 33
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 34
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 34
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 35

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.

Solution 35

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Chapter 16 – Permutations Exercise Ex. 16.4

Question 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

 

Question 3
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 3
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 4
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 4
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 5
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 5
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 11
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 11
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Chapter 16 – Permutations Exercise Ex. 16.5

Question 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 2
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 2
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 3
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 3
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 4
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 4
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 5
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 5
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 11
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 11
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 13
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 13
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 14
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 14
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 15

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 15

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 16

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 16

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 17

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 17

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 18

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 18

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 19

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 19

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 20

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 20

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 21

How many permulations of the letters of the world ‘MADHUBANI’ do not begain with M but end with I?

Solution 21

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 22

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 22

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 23

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 23

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 24

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 24

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 25

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 25

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 26

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 26

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 27

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 27

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 28

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 28

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 29

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 29

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 30

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 30

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 31

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 31

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 32

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 32

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 33

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 33

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 34

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 34

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 35

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 35

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Question 36

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 36

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Chapter 16 – Permutations Exercise Ex. 16VSAQ

Question 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 1
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 2
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 2
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 3
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 3
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 4
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 4
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 5
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 5
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 6
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 7
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 8
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 9
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 10
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 11

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

Solution 11

First we will find the least factorial term divisible by 14.

As 7!=7x6x5! is divisible by 14 leaving remainder zero.

 

Hence terms 7! onwards can be written as multiple of 7!.

8!=8×7!, 9!=9x8x7!… like ways 200! can also be written as multiple of 7!.

So all the terms 7! onwards are divisible by 14 leaving remainder zero.

 

1! + 2! + 3! + 4! + 5! + 6!

=1+2+6+24+120+720

=873

 

Hence remainder obtained when 1! + 2! + 3! + ….+ 200! is divided by 14 is 5.

Question 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 12
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Question 13
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations
Solution 13
Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Permutations

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