Quantrex Academy Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · JEE PYQs · Mathematics · Permutation and Combination

JEE Permutation and Combination PYQs with Solutions

503 previous year questions from Permutation and Combination (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

503 questionsMathematics2006–2026Answers + solutions

About Permutation and Combination PYQs

Permutation and Combination has 503 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (190) and JEE Advanced (30), spanning 2006 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 23
  • 2025: 21
  • 2024: 19
  • 2023: 42
  • 2022: 20
  • 2021: 27
  • 2020: 14
  • 2019: 14
  • 2018: 7
  • 2017: 4
  • 2016: 4
  • 2015: 7

Permutation and Combination questions with solutions

1

The number of ways to distribute 10 identical red pens and 14 identical blue pens among four persons such that each person gets 6 pens, is _____________.

JEE Advanced 2026 Solution View → 2

A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6 books are chosen at random. Let X be the absolute value of the

JEE Advanced 2026 Solution View → 3

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:

JEE Main 2026 Solution View → 4

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^ th floor. The number of ways, in which any 4 persons

JEE Main 2026 Solution View → 5

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

JEE Main 2026 Solution View → 6

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 :

JEE Main 2026 Solution View → 7

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

JEE Main 2026 Solution View → 8

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

JEE Main 2026 Solution View → 9

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

JEE Main 2026 Solution View → 10

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

JEE Main 2026 Solution View → 11

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 :

JEE Main 2026 Solution View → 12

Three persons enter in a lift at the ground floor. The lift will go upto 10^ th floor. The number of ways, in which the three persons can exit the lift at three different floors

JEE Main 2026 Solution View → 13

Let 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.

JEE Main 2026 Solution View → 14

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

JEE Main 2026 Solution View → 15

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

JEE Main 2026 Solution View → 16

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 \_\_\_\_

JEE Main 2026 Solution View → 17

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

JEE Main 2026 Solution View → 18

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(~S)+n(P) is equal to

JEE Main 2026 Solution View → 19

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

JEE Main 2026 Solution View → 20

Let ABC be a triangle. Consider four points p_ 1 , p_ 2 , p_ 3 , 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

JEE Main 2026 Solution View → 21

The largest n ∈ N , for which 7^ n divides 101!, is :

JEE Main 2026 Solution View → 22

The number of strictly increasing functions f from the set \ 1,2,3,4,5,6\ to the set \ 1,2,3, …., 9\ such that f(i) ≠ i for 1 ≤ i ≤ 6 , is equal to :

JEE Main 2026 Solution View → 23

Let S=\ (m, n): m, n ∈\ 1,2,3, ….., 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

JEE Main 2026 Solution View → 24

Let S be the set of all seven-digit numbers that can be formed using the digits 0,1 and 2 . For example, 2210222 is in S , but 0210222 is NOT in S . Then the number of elements x

JEE Advanced 2025 Solution View → 25

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

JEE Main 2025 Solution View → 26

Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the number of all quadrilaterals that can be formed by

JEE Main 2025 Solution View → 27

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

JEE Main 2025 Solution View → 28

For n ≥ 2 , let S_n denote the set of all subsets of \ 1,2 … . . ., n\ with no two consecutive numbers. For example \ 1,3,5\ ∈ S_6 , but \ 1,2,4\ ∉ S_6 . Then n(~S_5) is equal to

JEE Main 2025 Solution View → 29

Let m and n,(m n) be two 2-digit numbers. Then the total numbers of pairs (m, n) , such that gcd(m, n)=6 , is ________

JEE Main 2025 Solution View → 30

Line L_1 of slope 2 and line L_2 of slope (1)/(2) intersect at the origin O . In the first quadrant, P_1, P_2, … . P_ 12 are 12 points on line L_1 and Q_1, Q_2, … . . Q_9 are 9

JEE Main 2025 Solution View → 31

If the number of seven-digit numbers, such that the sum of their digits is even, is m · n · 10^ n ; m, n ∈\ 1,2,3, …, 9\ , then m+n is equal to _______

JEE Main 2025 Solution View → 32

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

JEE Main 2025 Solution View → 33

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

JEE Main 2025 Solution View → 34

The largest n ∈ N such that 3^ n divides 50 ! is:

JEE Main 2025 Solution View → 35

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 440^ th position in this arrangement, is

JEE Main 2025 Solution View → 36

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

JEE Main 2025 Solution View → 37

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

JEE Main 2025 Solution View → 38

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

JEE Main 2025 Solution View → 39

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

JEE Main 2025 Solution View → 40

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

JEE Main 2025 Solution View → 41

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 -

JEE Main 2025 Solution View → 42

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

JEE Main 2025 Solution View → 43

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

JEE Main 2025 Solution View → 44

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 :

JEE Main 2025 Solution View → 45

A group of 9 students, s_1, ~s_2, … …, s_9 , is to be divided to from three teams X, Y , and Z of sizes 2,3 , and 4 , respectively. Suppose that s_1 cannot be selected for the

JEE Advanced 2024 Solution View → 46

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

JEE Main 2024 Solution View → 47

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 :

JEE Main 2024 Solution View → 48

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__________

JEE Main 2024 Solution View → 49

Let 0 ≤ r ≤ 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:

JEE Main 2024 Solution View → 50

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^ th position in this arrangement is :

JEE Main 2024 Solution View → 51

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

JEE Main 2024 Solution View → 52

60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50^ th word is :

JEE Main 2024 Solution View → 53

The number of ways of getting a sum 16 on throwing a dice four times is______

JEE Main 2024 Solution View → 54

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is _____

JEE Main 2024 Solution View → 55

There are 5 points P_1, P_2, P_3, P_4, P_5 on the side A B , excluding A and B , of a triangle A B C . Similarly there are 6 points P_6, P_7, …, P_ 11 on the side BC and 7 points

JEE Main 2024 Solution View → 56

The lines L _ 1 , L _ 2 , . .. , L _ 20 are distinct. For n = 1, 2, 3, . .. , 10 all the lines L _ 2n - 1 are parallel to each other and all the lines L _ 2n pass through a given

JEE Main 2024 Solution View → 57

If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to:

JEE Main 2024 Solution View → 58

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

JEE Main 2024 Solution View → 59

The total number of words (with or without meaning) that can be formed out of the letters of the word "DISTRIBUTION" taken four at a time, is equal to ______.

JEE Main 2024 Solution View → 60

In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A, B and C . A student is required to attempt

JEE Main 2024 Solution View → 61

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

JEE Main 2024 Solution View → 62

All the letters of the word GTWENTY are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word GTWENTY

JEE Main 2024 Solution View → 63

Let α = ( 4 ! ) ! ( 4 ! ) ^ 3 ! and β = ( 5 ! ) ! ( 5 ! ) ^ 4 ! . Then :

JEE Main 2024 Solution View → 64

Let X be the set of all five digit numbers formed using 1, 2, 2, 2, 4, 4, 0 . For example, 22240 is in X while 02244 and 44422 are not in X . Suppose that each element of X has an

JEE Advanced 2023 Solution View → 65

Consider the 6 × 6 square in the figure. Let A _ 1 , A _ 2 , … , A _ 49 be the points of intersections (dots in the picture) in some order. We say that A _ i and A _ j are friends

JEE Advanced 2023 Solution View → 66

The total number of three-digit numbers, divisible by 3 , which can be formed using the digits 1, 3, 5, 8 , if repetition of digits is allowed, is

JEE Main 2023 Solution View → 67

A person forgets his 4 -digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to

JEE Main 2023 Solution View → 68

All words, with or without meaning, are made using all the letters of the word MONDAY . These words are written as in a dictionary with serial numbers. The serial number of the

JEE Main 2023 Solution View → 69

Total numbers of 3 -digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ________

JEE Main 2023 Solution View → 70

The number of seven digit positive integers formed using the digits 1, 2, 3 and 4 only and sum of the digits equal to 12 is _______ .

JEE Main 2023 Solution View → 71

The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 0, 1, 3, 5, 7 and 9 without repetition, is equal to

JEE Main 2023 Solution View → 72

Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How

JEE Main 2023 Solution View → 73

If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is

JEE Main 2023 Solution View → 74

The number of triplets (x, y, z) where x, y, z are distinct non negative integers satisfying x + y + z = 15 , is

JEE Main 2023 Solution View → 75

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is

JEE Main 2023 Solution View → 76

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which

JEE Main 2023 Solution View → 77

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to ____.

JEE Main 2023 Solution View → 78

The number of permutations, of the digits 1, 2, 3, … , 7 without repetition, which neither contain the string 153 nor the string 2467 , is _______ .

JEE Main 2023 Solution View → 79

Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840 , then the total numbers of

JEE Main 2023 Solution View → 80

If the number of words, with or without meaning. which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is ( 6 ! ) k then k is

JEE Main 2023 Solution View → 81

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is

JEE Main 2023 Solution View → 82

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together is

JEE Main 2023 Solution View → 83

The largest natural number n such that 3n divides 66 ! is _______

JEE Main 2023 Solution View → 84

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC

JEE Main 2023 Solution View → 85

The number of 4 -letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition

JEE Main 2023 Solution View → 86

The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is _____

JEE Main 2023 Solution View → 87

Number of integral solutions to the equation x + y + z = 21 , where x ≥ 1, y ≥ 3, z ≥ 4 , is equal to _____ .

JEE Main 2023 Solution View → 88

The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6 , is _____ .

JEE Main 2023 Solution View → 89

The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is _____ .

JEE Main 2023 Solution View → 90

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

JEE Main 2023 Solution View → 91

The number of ways of selecting two numbers a and b , a ∈ \ 2, 4, 6, … … , 100\ and b ∈ \ 1, 3, 5, … … , 99\ such that 2 is the remainder when a + b is divided by 23 is

JEE Main 2023 Solution View → 92

The number of seven digits odd numbers, that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is

JEE Main 2023 Solution View → 93

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

JEE Main 2023 Solution View → 94

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 :

JEE Main 2023 Solution View → 95

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

JEE Main 2023 Solution View → 96

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

JEE Main 2023 Solution View → 97

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

JEE Main 2023 Solution View → 98

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

JEE Main 2023 Solution View → 99

Suppose Anil&#39;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

JEE Main 2023 Solution View → 100

Let f ( x ) = 2 x ^ n + λ, λ ∈ ℝ, n ∈ ℕ , and f ( 4 ) = 133 , f ( 5 ) = 255 . Then the sum of all the positive integer divisors of ( f ( 3 ) - f ( 2 ) ) is

JEE Main 2023 Solution View → 101

Let x and y be distinct integers where 1 ≤ x ≤ 25 and 1 ≤ y ≤ 25 . Then, the number of ways of choosing x and y , such that x + y is divisible by 5 , is _____ .

JEE Main 2023 Solution View → 102

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 _____ .

JEE Main 2023 Solution View → 103

The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is

JEE Main 2023 Solution View → 104

A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways

JEE Main 2023 Solution View → 105

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 ______

JEE Main 2023 Solution View → 106

Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes

JEE Advanced 2022 Solution View → 107

The number of 4 -digit integers in the closed interval [2022, 4482] formed by using the digits 0, 2, 3, 4, 6, 7 is ______.

JEE Advanced 2022 Solution View → 108

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 _____.

JEE Main 2022 Solution View → 109

Let S = \ 4, 6, 9\ and T = \ 9, 10, 11, … , 1000\ . If A = \ a _ 1 + a _ 2 + … + a _ k : k ∈ N, a _ 1 , a _ 2 , a _ 3 , … , a _ k ∈ S\ then the sum of all the elements in the set

JEE Main 2022 Solution View → 110

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 + 3g is equal to

JEE Main 2022 Solution View → 111

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

JEE Main 2022 Solution View → 112

Numbers are to be formed between 1000 and 3000 , which are divisible by 4 , using the digits 1, 2, 3, 4, 5 and 6 without repetition of digits. Then the total number of such

JEE Main 2022 Solution View → 113

The number of 5 -digit natural numbers, such that the product of their digits is 36 , is

JEE Main 2022 Solution View → 114

The letters of the word &#39;MANKIND&#39; are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word

JEE Main 2022 Solution View → 115

The total number of four digit numbers such that each of the first three digits is divisible by the last digit, is equal to ______.

JEE Main 2022 Solution View → 116

Let b _ 1 b _ 2 b _ 3 b _ 4 be a 4 -element permutation with b _ i ∈ \ 1, 2, 3, … … … , 100\ for 1 ≤ i ≤ 4 and b _ i ≠ b _ j for i ≠ j , such that either b _ 1 , b _ 2 , b _ 3 are

JEE Main 2022 Solution View → 117

The number of ways to distribute 30 identical candies among four children C _ 1 , C _ 2 , C _ 3 and C _ 4 so that C _ 2 receives atleast 4 and atmost 7 candies, C _ 3 receives

JEE Main 2022 Solution View → 118

The total number of 5 -digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6 , is

JEE Main 2022 Solution View → 119

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is

JEE Main 2022 Solution View → 120

The total number of 3 -digit numbers, whose greatest common divisor with 36 is 2 , is ______.

JEE Main 2022 Solution View → 121

There are ten boys B _ 1 , B _ 2 , … . , B _ 10 and five girls G _ 1 , G _ 2 , … . G _ 5 in a class. Then the number of ways of forming a group consisting of three boys and three

JEE Main 2022 Solution View → 122

The total number of three-digit numbers, with one digit repeated exactly two times, is ______.

JEE Main 2022 Solution View → 123

The number of 3 -digit odd numbers, whose sum of digits is a multiple of 7 , is _____.

JEE Main 2022 Solution View → 124

The number of 7 -digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____.

JEE Main 2022 Solution View → 125

In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, - 2 marks for each wrong

JEE Main 2022 Solution View → 126

Let S _ 1 = \ (i, j, k): i, j, k ∈ \ 1, 2, … , 10\ \ S _ 2 = \ (i, j): 1 ≤ i S _ 3 = \ (i, j, k, l): 1 ≤ i and S _ 4 = \ (i, j, k, l): i, j, kandlare distint elements in\ 1, 2, .

JEE Advanced 2021 Solution View → 127

Let P _ 1 , P _ 2 … , P _ 15 be 15 points on a circle. The number of distinct triangles formed by points P _ i , P _ j , P _ k such that i + j + k ≠ 15, is :

JEE Main 2021 Solution View → 128

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the

JEE Main 2021 Solution View → 129

The number of 4 -digit numbers which are neither multiple of 7 nor multiple of 3 is .

JEE Main 2021 Solution View → 130

The number of six letter words (with or without meaning), formed using all the letters of the word &#39;VOWELS&#39;, so that all the consonants never come together, is

JEE Main 2021 Solution View → 131

Let S = 1, 2, 3, 4, 5, 6, 9 . Then the number of elements in the set T = A ⊆ S: A ≠ ϕ and the sum of all the elements of A is not a multiple of 3 is

JEE Main 2021 Solution View → 132

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are

JEE Main 2021 Solution View → 133

The sum of all 3 -digit numbers less than or equal to 500, that are formed without using the digit 1 and they all are multiple of 11, is ______.

JEE Main 2021 Solution View → 134

The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is______.

JEE Main 2021 Solution View → 135

Let n be a non-negative integer. Then the number of divisors of the form 4n + 1 of the number (10) ^ 10 · (11) ^ 11 · (13) ^ 13 is equal to _____.

JEE Main 2021 Solution View → 136

There are 5 students in class 10, 6 students in class 11 and 8 students in class 12 . If the number of ways, in which 10 students can be selected from them so as to include at

JEE Main 2021 Solution View → 137

If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10, 000 is equal to __________.

JEE Main 2021 Solution View → 138

The sum of all the elements in the set n ∈ 1, 2, … … , 100 ∣ H.C.F. of n and 2040 is 1 is equal to __________.

JEE Main 2021 Solution View → 139

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to

JEE Main 2021 Solution View → 140

The sum of all the 4 -digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is:

JEE Main 2021 Solution View → 141

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

JEE Main 2021 Solution View → 142

If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as

JEE Main 2021 Solution View → 143

Team A ' ' consists of 7 boys and n girls and Team B ' ' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a

JEE Main 2021 Solution View → 144

Consider a rectangle ABCD having 5, 6, 7, 9 points in the interior of the line segments AB, BC, CD, DA respectively. Let α be the number of triangles having these points from

JEE Main 2021 Solution View → 145

The total number of 4 -digit numbers whose greatest common divisor with 18 is 3 is _____.

JEE Main 2021 Solution View → 146

A natural number has prime factorization given by n = 2 ^ x 3 ^ y 5 ^ z , where y and z are such that y + z = 5 and y ^ - 1 + z ^ - 1 = (5)/(6), y > z . Then the number of odd

JEE Main 2021 Solution View → 147

The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is:

JEE Main 2021 Solution View → 148

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

JEE Main 2021 Solution View → 149

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

JEE Main 2021 Solution View → 150

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

JEE Main 2021 Solution View → 151

The students S _ 1 , S _ 2 , … , 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

JEE Main 2021 Solution View → 152

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

JEE Main 2021 Solution View → 153

An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two visits take place on consecutive days.

JEE Advanced 2020 Solution View → 154

In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two

JEE Advanced 2020 Solution View → 155

The number of words (with or without meaning) that can be formed from all the letters of the word " LETTER " in which vowels never come together is.....

JEE Main 2020 Solution View → 156

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not

JEE Main 2020 Solution View → 157

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section.

JEE Main 2020 Solution View → 158

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word &#39;SYLLABUS&#39; such that two letters are distinct

JEE Main 2020 Solution View → 159

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions

JEE Main 2020 Solution View → 160

The total number of 3 - digit numbers whose sum of digits is 10 , is ..........

JEE Main 2020 Solution View → 161

Let n > 2 be an integer. Suppose that there are n Metro stations in a city located around a circular path. Each pair of the nearest stations is connected by a straight track only.

JEE Main 2020 Solution View → 162

If the letters of the word ^ ' MOTHER ^ ' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word ' MOTHER ^

JEE Main 2020 Solution View → 163

If the number of five digit numbers with distinct digits and 2 at the 10 ^ th place is 336k , then k is equal to:

JEE Main 2020 Solution View → 164

The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is

JEE Main 2020 Solution View → 165

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then, the number of ways in which 4 marbles can be drawn so that at the most three of them are red is

JEE Main 2020 Solution View → 166

Total number of 6 - digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appears, is

JEE Main 2020 Solution View → 167

Five persons A, B, C, D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then the number of ways of

JEE Advanced 2019 Solution View → 168

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one

JEE Main 2019 Solution View → 169

The Number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:

JEE Main 2019 Solution View → 170

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:

JEE Main 2019 Solution View → 171

Suppose that 20 pillars of the same height have been erected along the boundary of circular stadium. If the top of each pillar has been connected by beams with the top of all its

JEE Main 2019 Solution View → 172

The number of 6 digit number that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is:

JEE Main 2019 Solution View → 173

A committee of 11 member is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the

JEE Main 2019 Solution View → 174

The number of four-digit numbers strictly greater than 4321 that can be formed using the digit 0,1, 2,3, 4,5 (repetition of digits is allowed) is:

JEE Main 2019 Solution View → 175

All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is

JEE Main 2019 Solution View → 176

There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between

JEE Main 2019 Solution View → 177

Let S = \ 1, 2, 3, … . , 100\ , then number of non-empty subsets A of S such that the product of elements in A is even is :

JEE Main 2019 Solution View → 178

Consider three boxes, each containing 10 balls labelled 1, 2, … . , 10 . Suppose one ball is randomly drawn from each of the boxes. Denote by n _ i , the label of the ball drawn

JEE Main 2019 Solution View → 179

The number of natural numbers less than 7000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to:

JEE Main 2019 Solution View → 180

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B

JEE Main 2019 Solution View → 181

In a high school, a committee has to be formed from a group of 6 boys M _ 1 , M _ 2 , M _ 3 , M _ 4 , M _ 5 , M _ 6 and 5 girls G _ 1 , G _ 2 , G _ 3 , G _ 4 , G _ 5 . (i) Let α _

JEE Advanced 2018 Solution View → 182

The number of 5 digit numbers which are divisible by 4 , with digits from the set 1,2, 3,4, 5 and the repetition of digits is allowed, is _____.

JEE Advanced 2018 Solution View → 183

The number of numbers between 2, 000 and 5, 000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is

JEE Main 2018 Solution View → 184

The number of four letter words that can be formed using the letters of the word BARRACK is

JEE Main 2018 Solution View → 185

n - digit numbers are formed using only three digits 2,5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed, is

JEE Main 2018 Solution View → 186

n -digit numbers are formed using only three digits 2, 5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed is :

JEE Main 2018 Solution View → 187

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle.

JEE Main 2018 Solution View → 188

Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated; and let y be the number of such words

JEE Advanced 2017 Solution View → 189

The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B _ 1 and a particular girl G _ 1 never sit adjacent to each other, is:

JEE Main 2017 Solution View → 190

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:

JEE Main 2017 Solution View → 191

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total

JEE Main 2017 Solution View → 192

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team.

JEE Advanced 2016 Solution View → 193

If ^ n + 2 C _ 6 ^ n - 2 P _ 2 = 11 , then n satisfies the equation:

JEE Main 2016 Solution View → 194

If the four letter words (need not be meaningful) are to be formed using the letters from the word &quot;MEDITERRANEAN&quot; such that the first letter is R and the fourth letter

JEE Main 2016 Solution View → 195

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is

JEE Main 2016 Solution View → 196

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in

JEE Advanced 2015 Solution View → 197

Let A = \ x _ 1 , x _ 2 , … , x _ 7 \ andB = \ y _ 1 , y _ 2 , y _ 3 \ be two sets containing seven and three distinct elements respectively. Then the total number of functions f

JEE Main 2015 Solution View → 198

If in a regular polygon the number of diagonals is 54 , then the number of sides of this polygon is:

JEE Main 2015 Solution View → 199

The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman is

JEE Main 2015 Solution View → 200

The number of integers greater than 6000 that can be formed, using the digits 3, 5, 6, 7 and 8 , without repetition is

JEE Main 2015 Solution View →
Practice all Permutation and Combination questions in the app →

Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Permutation and Combination in other exams

NDA Permutation and Combination (129)BITSAT Permutation and Combination (31)