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

E M B I B E

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

HARD

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IMPORTANT

Earn 100

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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Important Questions on Permutation and Combination

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 1>Q 6

Let

E (n)

denote the sum of the even digits of

n .

For example,

E (1243) = 2 + 4 = 6 .

What is the value of

\frac{E (1) + E (2) + E (3) + \dots \dots . + E (100)}{100}

?

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 1>Q 7

A subset

B

of the set of first

100

positive integers has the property that no two elements of

B

sum to

125 .

What is the maximum possible number of elements in B?

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 1>Q 8

At a party, each man danced with exactly four women and each woman danced with exactly three men. Nine men attended the party. How many women attended the party?

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 1>Q 9

Kumar never lies except on Tuesdays. On Tuesdays, he always lies. On how many days of the week can he say "If I did not lie yesterday then I will lie tomorrow" ?

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IMPORTANT

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

is

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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