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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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 Questions on Permutation and Combination

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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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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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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)

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 12

All diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the boundary) do two or more diagonals intersect?

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 13

If from the set

1, 2, 3, . . ., 2017

, the number of ways in which one can choose two different numbers whose sum is an even number be

n

, then

n - 1016000

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 14

There are

12

intermediate stations on a railway line from one terminus to another. The number of ways in which a train can stop at

5

of these intermediate stations, if no two of these stopping stations are to be consecutive is

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 15

Let

y

be an element of

A = \{1, 2, 3, 5, 6, 10, 15, 30\}

, and

x_{1}, x_{2}, x_{3}

be integers such that

x_{1} x_{2} x_{3} = y,

then the number of positive integral solutions of

x_{1} x_{2} x_{3} = y

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 16

Seven cards and seven envelopes are numbered

1, 2, 3, 4, 5, 6, 7

and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card number

1

is always placed in envelope number

2

and

2

is always placed in envelope numbered

3,

then the number of ways it can be done is

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)

Important Questions on Permutation and Combination

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