EASY

JEE Main

IMPORTANT

Earn 100

The number of square matrices of order $5$ with entries from the set ${0, 1}$ , such that the sum of all the elements in each row is $1$ and the sum of all the elements in each column is also $1$ , is

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Important Questions on Permutation and Combination

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 January 2023 Shift 1>Q 111

Let

S = \{1, 2, 3, 5, 7, 10, 11\}

. The number of non-empty subsets of

S

that have the sum of all elements a multiple of

3

, is _____ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 January 2023 Shift 1>Q 112

Let

x

and

y

be distinct integers where

1 \leq x \leq 25

and

1 \leq y \leq 25

. Then, the number of ways of choosing

x

and

y

, such that

x + y

is divisible by

5

, is _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 January 2023 Shift 2>Q 113

The number of numbers, strictly between $5000$ and $10000$ can be formed using the digits $1, 3, 5, 7, 9$ without repetition, is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 January 2023 Shift 2>Q 114

\sum_{k = 0}^{6} {}^{51 - k}C_{3}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 January 2023 Shift 2>Q 115

Suppose Anil's mother wants to give

5

whole fruits to Anil from a basket of

7

red apples,

5

white apples and

8

oranges. If in the selected

5

fruits, at least

2

orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer

5

fruits to Anil is _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 29 January 2023 Shift 1>Q 116

If all the six digit numbers

x_{1} x_{2} x_{3} x_{4} x_{5} x_{6}

with

0 < x_{1} < x_{2} < x_{3} < x_{4} < x_{5} < x_{6}

are arranged in the increasing order, then the sum of the digits in the

72^{th}

number is _______.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 29 January 2023 Shift 1>Q 117

Five digit numbers are formed using the digits

1, 2, 3, 5, 7

with repetitions and are written in descending order with serial numbers. For example, the number

77777

has serial number

1

. Then the serial number of

35337

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 29 January 2023 Shift 2>Q 118

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is :

The number of square matrices of order 5 with entries from the set {0,1}, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is

Important Questions on Permutation and Combination

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The number of square matrices of order $5$ with entries from the set ${0, 1}$ , such that the sum of all the elements in each row is $1$ and the sum of all the elements in each column is also $1$ , is