Permutations and Combinations PYQs - Last 10 Years

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Practice 193 JEE Main Mathematics questions from Permutations and Combinations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Mathematics / Algebra

2017-2026

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132

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2022-2026

193

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2017-2026

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193PYQs

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INTEGER48.2%

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#1 Medium150

#2 Easy32

#3 Hard11

132 in last 5 years193 in last 10 years

Last 10 Years Permutations and Combinations Questions

Showing 50 of 193 filtered questions.

1Permutations And Combinations

A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is :

2Permutations And Combinations

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:

3Permutations And Combinations

A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the $10^{\text {th }}$ floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit ...

4Permutations And Combinations

Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is $\_\_\_\_$ .

INTEGER+4 / -12026

5Permutations And Combinations

A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is :

6Permutations And Combinations

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

7Permutations And Combinations

Let
$\mathrm{A}=\{(a, b, c): a, b, c$ are non-negative integers and $a+b+2 c=22\}$.
Then $n(\mathrm{~A})$ is equal to :

8Permutations And Combinations

The number of elements in the set $S = \left\{ (r, k) : k \in \mathbb{Z} \text{ and } ^{36}C_{r+1} = \frac{6\left(^{35}C_{r}\right)}{(k^2-3)} \right\}$ is :

9Permutations And Combinations

The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is:

10Permutations And Combinations

Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-side regular polygon.If $p_{n+1} - p_n = 66$, then the sum of all distinct prime divisors of $n$ is :

11Permutations And Combinations

Let $\mathrm{S}=\{1,2,3,4,5,6,7,8,9\}$. Let $x$ be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let $y$ be the number of 9 -digit numbers formed us...

12Permutations And Combinations

Three persons enter in a lift at the ground floor. The lift will go up to 10th floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, i...

INTEGER+4 / -12026

13Permutations And Combinations

The number of numbers greater than 5000 , less than 9000 and divisible by 3 , that can be formed using the digits $0,1,2,5,9$, if the repetition of the digits is allowed, is $\_\_\_\_$

INTEGER+4 / -12026

14Permutations And Combinations

The largest value of $n$, for which $40^n$ divides $60!$, is

15Permutations And Combinations

The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is

16Permutations And Combinations

The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is $\_\_\_\_$ .

INTEGER+4 / -12026

17Permutations And Combinations

Let S denote the set of 4-digit numbers $a b c d$ such that $a>b>c>d$ and P denote the set of 5 -digit numbers having product of its digits equal to 20 . Then $n(\mathrm{~S})+n(\mathrm{P})$ is equal to $\_\_\_\_$

INTEGER+4 / -12026

18Permutations And Combinations

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

19Permutations And Combinations

Let ABC be a triangle. Consider four points $\mathrm{p}_1, \mathrm{p}_2, \mathrm{p}_3, \mathrm{p}_4$ on the side AB , five points $p_5, p_6, p_7, p_8, p_9$ on the side $B C$, and four points $p_{10}, p_{11}, p_{12}, p_{13}$ on the side AC ....

INTEGER+4 / -12026

20Permutations And Combinations

Let $S=\{(m, n): m, n \in\{1,2,3, \ldots . ., 50\}\}$. If the number of elements $(m, n)$ in $S$ such that $6^m+9^n$ is a multiple of 5 is $p$ and the number of elements ( $m, n$ ) in $S$ such that $m+n$ is a square of a prime number is q ,...

INTEGER+4 / -12026

21Permutations And Combinations

The number of strictly increasing functions $f$ from the set $\{1,2,3,4,5,6\}$ to the set $\{1,2,3, \ldots ., 9\}$ such that $f(i) \neq i$ for $1 \leq i \leq 6$, is equal to :

22Permutations And Combinations

The largest $n \in \mathbb{N}$, for which $7^n$ divides $101!$, is :

23Permutations And Combinations

There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is

24Permutations And Combinations

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be in...

25Permutations And Combinations

Let m and $\mathrm{n},(\mathrm{m}<\mathrm{n})$, be two 2-digit numbers. Then the total numbers of pairs $(\mathrm{m}, \mathrm{n})$, such that $\operatorname{gcd}(m, n)=6$, is __________ .

INTEGER+4 / -12025

26Permutations And Combinations

If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^n ; m, n \in\{1,2,3, \ldots, 9\}$, then $m+n$ is equal to__________

INTEGER+4 / -12025

27Permutations And Combinations

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by $\mathrm{W}_{\mathrm{n}}$. Let the probability $\mathrm{P}\left...

INTEGER+4 / -12025

28Permutations And Combinations

Line $L_1$ of slope 2 and line $L_2$ of slope $\frac{1}{2}$ intersect at the origin O . In the first quadrant, $\mathrm{P}_1$, $P_2, \ldots, P_{12}$ are 12 points on line $L_1$ and $Q_1, Q_2, \ldots, Q_9$ are 9 points on line $L_2$. Then th...

29Permutations And Combinations

The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1 s and exactly three 2 s , is equal to :

30Permutations And Combinations

The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is :

31Permutations And Combinations

The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is _________.

INTEGER+4 / -12025

32Permutations And Combinations

Let $ P $ be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in $ P $ are formed by using the digits 1, 2 and 3 only, then the number of elements in the set $ P $ is :

33Permutations And Combinations

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th position in this arrangement is :

34Permutations And Combinations

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , $1,2,3,4,5,6,7$, such that the sum of their first and last digits should not be more than 8 , is

35Permutations And Combinations

Let ${ }^n C_{r-1}=28,{ }^n C_r=56$ and ${ }^n C_{r+1}=70$. Let $A(4 \operatorname{cost}, 4 \sin t), B(2 \sin t,-2 \cos t)$ and $C\left(3 r-n, r^2-n-1\right)$ be the vertices of a triangle $A B C$, where $t$ is a parameter. If $(3 x-1)^2+(3...

36Permutations And Combinations

The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is _______.

INTEGER+4 / -12025

37Permutations And Combinations

The number of 3 -digit numbers, that are divisible by 2 and 3 , but not divisible by 4 and 9 , is _________.

INTEGER+4 / -12025

38Permutations And Combinations

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group $A$ and the remaining 3 from group $B$, is equal to :

39Permutations And Combinations

Number of functions $f:\{1,2, \ldots, 100\} \rightarrow\{0,1\}$, that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to ________.

INTEGER+4 / -12025

40Permutations And Combinations

The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is :

41Permutations And Combinations

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is ________.

INTEGER+4 / -12025

42Permutations And Combinations

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :

43Permutations And Combinations

In a group of 3 girls and 4 boys, there are two boys $B_1$ and $B_2$. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $B_1$ and $B_2$ are not ad...

44Permutations And Combinations

The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is __________.

INTEGER+4 / -12024

45Permutations And Combinations

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to ________.

INTEGER+4 / -12024

46Permutations And Combinations

Let \([t]\) be the greatest integer less than or equal to \(t\). Let \(A\) be the set of all prime factors of 2310 and \(f: A \rightarrow \mathbb{Z}\) be the function \(f(x)=\left[\log _2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right]\)....

47Permutations And Combinations

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to:

48Permutations And Combinations

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

49Permutations And Combinations

Let \(0 \leq r \leq n\). If \({ }^{n+1} C_{r+1}:{ }^n C_r:{ }^{n-1} C_{r-1}=55: 35: 21\), then \(2 n+5 r\) is equal to :

50Permutations And Combinations

If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at \(315^{\text {th }}\) position in this arrangement is :