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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All the five-digit numbers $N = a b c d e$ having the property $a < b < c < d < e$ are arranged in the increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit

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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 2>Q 20

There are two sets of parallel lines. Their equations are

x \cos α + y \sin α = p

and

x \sin α - y \cos α = p

;

p = 1, 2, 3 \dots n

and

α \in (0, \frac{π}{2}) .

If the number of rectangles formed by these two sets of lines is

225

, then the value of

n

is equal to

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 2>Q 21

A set of

16

square blocks is arranged into a

4 \times 4

square. If the number of combinations of

3

blocks that can be selected from that set so that no two are in the same row or column is

m

, then

\frac{m}{4}

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 2>Q 22

Let

(a_{1}, a_{2}, \dots, a_{10})

be a list of the first

10

positive integers such that for each

2 \leq i \leq 10

either

a_{i} + 1

a_{i} - 1

or both appear somewhere before

a_{i}

in the list. If number of such lists are

2^{k},

find

k .

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 2>Q 23

What is the number of ways in which one can colour the squares of a

4 \times 4

chessboard with colours red and blue such that each row as well as each column has exactly two red squares and two blue squares?

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 2>Q 24

There are

n - 1

red balls,

n

green balls and

n + 1

blue balls in a bag. The number of ways of choosing two balls from the bag that have different colours is

299 .

What is the value of

n

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 2>Q 25

A B C D

is a convex quadrilateral and

3, 4, 5

and

6

points are marked on the sides

A B, B C, C D

and

D A,

respectively. The number of triangles with vertices on different sides is (none of them is

A, B, C

D

)

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 2>Q 26

A team of four students is to be selected from a total of

12

students. Total number of ways in which team can be selected such that two particular students refuse to be together and other two particular students wish to be together only, is equal to

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 2>Q 27

The number of ways of distributing

3

identical physics books and

3

identical mathematics books among three students such that each student gets at least one book is

All the five-digit numbers N=abcde having the property a<b<c<d<e are arranged in the increasing order of their magnitude. The 97th number in the list does not contain the digit

Important Questions on Permutation and Combination

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All the five-digit numbers $N = a b c d e$ having the property $a < b < c < d < e$ are arranged in the increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit