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JEE Main

IMPORTANT

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Let $S$ be the set containing all $3 \times 3$ matrices with entries from $\{- 1, 0, 1\}$ . The total number of matrices $A \in S$ such that the sum of all the diagonal elements of $A^{T} A$ is $6$ 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 - 27 July 2022 Shift 2>Q 100

The number of functions

f

, from the set

A = \{x \in N : x^{2} - 10 x + 9 \leq 0\}

to the set

B = \{n^{2} : n \in N\}

such that

f (x) \leq {(x - 3)}^{2} + 1

, for every

x \in A

, is _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 28 July 2022 Shift 1>Q 101

Let

S

be the set of all passwords which are six to eight characters long, where each character is either an alphabet from

\{A, B, C, D, E\}

or a number from

\{1, 2, 3, 4, 5\}

with the repetition of characters allowed. If the number of passwords in

S

whose at least one character is a number from

\{1, 2, 3, 4, 5\}

α \times 5^{6}

, then

α

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 28 July 2022 Shift 2>Q 102

A class contains

b

boys and

g

girls. If the number of ways of selecting

3

boys and

2

girls from the class is

168

, then

b + 3 g

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 29 July 2022 Shift 1>Q 103

The number of matrices of order

3 \times 3

, whose entries are either

0

1

and the sum of all the entries is a prime number, is _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 29 July 2022 Shift 2>Q 104

The number of natural numbers lying between

1012

and

23421

that can be formed using the digits

2, 3, 4, 5, 6

(repetition of digits is not allowed) and divisible by

55

is _____.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 24 January 2023 Shift 1>Q 105

The value of

\sum_{r = 0}^{22} {}^{22}C_{r} \cdot {}^{23}C_{r}

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 24 January 2023 Shift 1>Q 106

Suppose

\sum_{r = 0}^{2023} r^{2} \cdot {}^{2023}C_{r} = 2023 \times α \times 2^{2022}

, then the value of

α

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 24 January 2023 Shift 1>Q 107

The number of

9

digit numbers, that can be formed using all the digits of the number

123412341

so that the even digits occupy only even places, is ______

Let S be the set containing all 3×3 matrices with entries from -1,0,1. The total number of matrices A∈S such that the sum of all the diagonal elements of ATA is 6 is ______.

Important Questions on Permutation and Combination

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Let $S$ be the set containing all $3 \times 3$ matrices with entries from $\{- 1, 0, 1\}$ . The total number of matrices $A \in S$ such that the sum of all the diagonal elements of $A^{T} A$ is $6$ is ______.