EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 29 January 2023 Shift 2>Q 120

HARD

JEE Main

IMPORTANT

Earn 100

The total number of $4$ -digit numbers whose greatest common divisor with $54$ is $2$ , is

50% studentsanswered this correctly

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 - 30 January 2023 Shift 1>Q 121

Let

S = {1, 2, 3, 4, 5, 6}

. Then the number of one-one functions

f : S \to P (S)

, where

P (S)

denote the power set of

S

, such that

f (n) \subset f (m)

where

n < m

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 30 January 2023 Shift 1>Q 122

Number of

4

-digit numbers (the repetition of digits is allowed) which are made using the digits

1, 2, 3

and

5

, and are divisible by

15

, is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 30 January 2023 Shift 2>Q 123

The number of ways of selecting two numbers

a

and

b

,

a \in \{2, 4, 6, \dots \dots, 100\}

and

b \in \{1, 3, 5, \dots \dots, 99\}

such that

2

is the remainder when

a + b

is divided by

23

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 30 January 2023 Shift 2>Q 124

The number of seven digits odd numbers, that can be formed using all the seven digits

1, 2, 2, 2, 3, 3, 5

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 31 January 2023 Shift 1>Q 125

Let

5

digit numbers be constructed using the digits

0, 2, 3, 4, 7, 9

with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number

42923

is _____ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 31 January 2023 Shift 1>Q 126

Number of

4

-digit numbers that are less than or equal to

2800

and either divisible by

3

or by

11

, is equal to _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 31 January 2023 Shift 2>Q 127

If

{}^{2 n + 1}P_{n - 1} : {}^{2 n - 1}P_{n} = 11 : 21

, then

n^{2} + n + 15

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 1 February 2023 Shift 1>Q 128

The number of

3

-digit numbers, that are divisible by either

2

or

3

but not divisible by

7

is _____ .