The missing value in the following figure is

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 18 March 2021 Shift 2>Q 23

If $\sum _{r=1}^{10}r!\left(r^3+6r^2+2r+5\right)=\alpha \left(11!\right)$, then the value of $\alpha$ is equal to ___ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 24 Feb 2021 Shift 1>Q 24

A scientific committee is to be formed from $6$ Indians and $8$ foreigners, which includes at least $2$ Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 24 Feb 2021 Shift 2>Q 25

The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 24 Feb 2021 Shift 2>Q 26

The students $S_1,S_2,\dots ,S_{10}$ are to be divided into $3$ groups $A, B$ and $C$ such that each group has at least one student and the group $C$ has at most $3$ students. Then the total number of possibilities of forming such groups is __________.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 Feb 2021 Shift 1>Q 27

The total number of positive integral solutions $\left(x, y, z\right)$ such that $xyz=24$ is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 Feb 2021 Shift 1>Q 28

The total number of numbers, lying between $100$ and $1000$ that can be formed with the digits $1,2,3,4,5,$ if the repetition of digits is not allowed and numbers are divisible by either $3$ or $5,$ is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 Feb 2021 Shift 2>Q 29

Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A\times B$. Then :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 Feb 2021 Shift 2>Q 30

The total number of two digit numbers $\text{'}n\text{'}$, such that $3^n+7^n$ is a multiple of $10$ , is ___ .