EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Permutation and Combination>JEE Advanced Paper 2 - 2018>Q 6

HARD

JEE Advanced

IMPORTANT

Earn 100

Let $X$ be a set with exactly $5$ elements and $Y$ be a set with exactly $7$ elements. If $α$ is the number of one-one functions from $X \to Y$ and $β$ is the number of onto functions from $Y \to X$ , then the value of $\frac{1}{5!} (β - α)$ is _____-.

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Important Questions on Permutation and Combination

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Permutation and Combination>JEE Advanced Paper 2 - 2017>Q 8

Let

S = \{1,2, 3, \dots . 9\}

. For

k = 1,2, \dots 5,

let

N_{k}

be the number of subsets of

S

, each containing five elements out of which exactly

k

are odd. Then

N_{1} + N_{2} + N_{3} + N_{4} + N_{5} =

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Permutation and Combination>JEE Advanced Paper 2 - 2014>Q 9

Six cards and six envelopes are numbered

1, 2, 3, 4, 5, 6

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 more over the card numbered

1

is always placed in envelope numbered

2

. Then the number of ways it can be done is

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JEE Advanced

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Permutation and Combination>JEE Advanced Paper 1 - 2018>Q 10

The number of

5

digit numbers which are divisible by

4

, with digits from the set

{1,2, 3,4, 5}

and the repetition of digits is allowed, is _____.

MEDIUM

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Permutation and Combination>JEE Advanced Paper 1 - 2016>Q 12

A debate club consists of

6

girls and

4

boys. A team of

4

members is to be selected from this club including the selection of a captain (from among these

4

members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is