Three and four digit numbers are formed from the digits 1 , 3 , 5 , 6 , 8 . If e 1 is number of three digit even numbers with no digit repeated and e 2 is number of four digit even numbers with no digit repeated. Also O 1 represent the number of three digit odd numbers in which no digit is repeated and O 2 represent the number of four digit odd numbers in which no digit is repeated. Then

e 1 + e 2 2 = O 1 + O 2 3 = 6 2

e 1 + e 2 + O 1 + O 2 = 5 P 3 + 5 3

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IMPORTANT

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If there are $N$ integers between $100$ and $999$ , inclusive, have the property that some permutation of its digits is a multiple of $11$ between $100$ and $999 ?$ For example, both $121$ and $231$ have this property. Then find the value of $\frac{N - 1}{5} .$

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Important Questions on Permutation and Combination

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 4

Five persons wearing badges with numbers

1, 2, 3, 4, 5

are seated on

5

chairs around a circular table. In how many ways can they be seated so that no two persons whose badges have consecutive numbers are seated next to each other? (Two arrangements obtained by rotation around the table are considered different.)

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 5

The value of

\sum_{r = 0}^{50} {(- 1)}^{r} \frac{{}^{50}C_{r}}{r + 2}

is equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 6

A seven-digit number is in the form of

a b c d e f g

(

g, f, e \dots

etc.,, are digits at the units, tens, hundred place, and so on), where

a < b < c < d > e > f > g

and

a, b, c, e, f, g

are different digits. The number of such numbers is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 7

A guard of

12

men is formed from a group of

n

soldiers. It is found that

2

particular soldiers

A

and

B

are

3

times as often together on guard as

3

particulars soldiers

C, D

and

E

. Then

n

is equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 8

The number of permutations of $1, 2, 3, 4, 5, 6, 7, 8$ and $9$ taken all at a time, such that digit $1$ appears some where to the left of digit $2$ and digit $3$ appears to the left of digit $4$ and digit $5$ appears some where to the left of digit $6$ , is (e.g. $815723946$ would be one such permutation)

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 9

The number of pairs of the diagonals of a regular polygon of

10

sides that are parallel is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 10

The number of increasing functions from

f : A \to B

, where

A \in \{a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}\}, B \in {1, 2, 3 \dots 9}

, such that

a_{i + 1} > a_{i} \forall i \in N

and

a_{i} \neq i

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 11

Let

a_{1}, a_{2}, a_{3}, \dots

be the sequence of all positive integers that are relatively prime to

75

, where

a_{1} < a_{2} < a_{3} < \dots .

(The first five terms of the sequence are:

a_{1} = 1, a_{2} = 2, a_{3} = 4, a_{4} = 7, a_{5} = 8 .

)
Then the value of

a_{2008}

is defined as

p \cdot 10^{3} + q \cdot 10^{2} + r \cdot 10 + s

. Find

(p + q + r + s)

If there are N integers between 100 and 999, inclusive, have the property that some permutation of its digits is a multiple of 11 between 100 and 999? For example, both 121 and 231 have this property. Then find the value of N-15.

Important Questions on Permutation and Combination

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If there are $N$ integers between $100$ and $999$ , inclusive, have the property that some permutation of its digits is a multiple of $11$ between $100$ and $999 ?$ For example, both $121$ and $231$ have this property. Then find the value of $\frac{N - 1}{5} .$