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Permutation and Combination — NDA Mathematics PYQs

129 previous year questions from Permutation and Combination with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

129 questionsMathematicsSolutions on every page
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Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that t

NDA 2026 Solution View → 2

How many numbers greater than 1000 can be formed using the digits 0 , 1 , 2 and 3 (repetition of digits is not allowed) ?

NDA 2026 Solution View → 3

What is the maximum number of points of intersection of 5 circles ?

NDA 2026 Solution View → 4

Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that t

NDA 2026 Solution View → 5

Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that t

NDA 2026 Solution View → 6

If n= ^ m C₂ then what is ^ n C₂ equal to ?

NDA 2026 Solution View → 7

Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that t

NDA 2026 Solution View → 8

How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is not allowed)?

NDA 2025 Solution View → 9

For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear. How many quadrilaterals can be formed by joining these points?

NDA 2025 Solution View → 10

Let y = x! and z = (2x)! . If (z/y) = 120 , then what is the value of (3x)! ?

NDA 2025 Solution View → 11

In how many ways can the letters of the word DELHI be arranged keeping the positions of vowels and consonants unchanged?

NDA 2025 Solution View → 12

How many sides are there in a polygon which has 20 diagonals?

NDA 2025 Solution View → 13

How many 7-letter words (with or without meaning) can be constructed using all the letters of the word CAPITAL so that all consonants come together in each word?

NDA 2025 Solution View → 14

What is the number of selections of at most 3 things from 6 different things?

NDA 2025 Solution View → 15

For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear. How many triangles can be formed by joining these points?

NDA 2025 Solution View → 16

Let n be a natural number. The number of consecutive zeros at the end of the expansion of n! is exactly 2. How many values of n are possible?

NDA 2025 Solution View → 17

If the number of selections of r as well as (n+r) things from 5n different things are equal, then what is the value of r ?

NDA 2025 Solution View → 18

What is the number of positive integer solutions of x + y + z = 5 ?

NDA 2025 Solution View → 19

How many 4-digit numbers are there having all digits as odd?

NDA 2024 Solution View → 20

In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?

NDA 2024 Solution View → 21

The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

NDA 2024 Solution View → 22

The letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternatively?

NDA 2024 Solution View → 23

Three perfect dice D ₁, D ₂ and D ₃ are rolled. Let x, y and z represent the numbers on D ₁, D ₂ and D ₃ respectively. What is the number of possible outcomes such that x < y < z ?

NDA 2024 Solution View → 24

What is the sum of all four digit numbers formed by using all digits 0,1,4,5 without repetition of digits?

NDA 2024 Solution View → 25

A man has 7 relatives ( 4 women and 3 men). His wife also has 7 relatives ( 3 women and 4 men). In how many ways can they invite 3 women and 3 men so that 3 of them are man's relat

NDA 2024 Solution View → 26

If 26!= _n 8^k , where k and n are positive integers, then what is the maximum value of k ?

NDA 2024 Solution View → 27

A triangle PQR is such that 3 points lie on the side PQ , 4 points on QR and 5 points on R P respectively. Triangles are constructed using these points as vertices. What is the num

NDA 2024 Solution View → 28

How many four-digit natural numbers are there such that all of the digits are even?

NDA 2024 Solution View → 29

Four digit numbers are formed by using the digits 1,2,3,5 without repetition of digits. How many of them are divisible by 4 ?

NDA 2024 Solution View → 30

In how many ways can a student choose (n-2) courses out of n courses if 2 courses are compulsory (n>4) ?

NDA 2024 Solution View → 31

What is the maximum number of points of intersection of 10 circles?

NDA 2023 Solution View → 32

Three boys, P, Q, R an three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that all three boys sit together?

NDA 2023 Solution View → 33

Three boys, P, Q, R an three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that no two girls sit together?

NDA 2023 Solution View → 34

Paragraph: Consider the sum S =0!+1!+2!+3!+4!+ +100!34 Question: If the sum S is divided by 8 , what is the remainder?

NDA 2023 Solution View → 35

Let x be the number of permutations of the word 'PERMUTATIONS' and y be the number of permutations of the word 'COMBINATIONS'. Which one of the following is correct?

NDA 2023 Solution View → 36

5 - digit numbers are formed using the digits 0,1,2,4,5 without repetition. What is the percentage of numbers which are greater than 50,000 ?

NDA 2023 Solution View → 37

m parallel lines cut n parallel lines giving rise to 60 parallelograms. What is the value of (m+n) ?

NDA 2023 Solution View → 38

What is the number of 6 digit numbers that can be formed only by using 0,1,2,3,4 and 5 (each once); and divisible by 6 ?

NDA 2023 Solution View → 39

How many four-digit natural numbers are there such that all of the digits are odd?

NDA 2022 Solution View → 40

If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) are there in the list before the first wo

NDA 2022 Solution View → 41

Paragraph: Consider the word 'QUESTION' : Question: How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed ?

NDA 2022 Solution View → 42

A box contains 2 white balls, 3 black balls and 4 red balls. What is the number of ways of drawing 3 balls from the box with at least one black ball?

NDA 2022 Solution View → 43

Paragraph: Consider the word 'QUESTION' : Question: How many 8 -letter words with or without meaning, can be formed so that all consonants are together?

NDA 2022 Solution View → 44

Paragraph: Consider the word 'QUESTION' : Question: How many 8 -letter words with or without meaning, can be formed such that consonants and vowels occupy alternate positions?

NDA 2022 Solution View → 45

How many odd numbers between 300 and 400 are there in which none of the digits is repeated?

NDA 2022 Solution View → 46

How many permutations are there of the letters of the word 'TIGER' in which the vowels should not occupy the even positions?

NDA 2022 Solution View → 47

If C(3 n, 2 n)=C(3 n, 2 n-7) , then what is the value of C(n, n-5) ?

NDA 2022 Solution View → 48

What is the maximum value of n such that 5^n divides (30! +35 !), where n is a natural number?

NDA 2022 Solution View → 49

In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players?

NDA 2022 Solution View → 50

If C(n, 4), C(n, 5) and C(n, 6) are in AP, then what is the value of n ?

NDA 2021 Solution View → 51

Let S= 2,3,4,5,6,7,9 . How many different 3-digit numbers (with all digits different) from S can be made which are less than 500 ?

NDA 2021 Solution View → 52

Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct? 1. The number of straight lines that can be drawn by joining any two o

NDA 2021 Solution View → 53

Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?

NDA 2021 Solution View → 54

In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?

NDA 2021 Solution View → 55

Consider the digits 3,5,7,9 . What is the number of 5 -digit numbers formed by these digits in which each of these four digits appears?

NDA 2021 Solution View → 56

How many 4-letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of the word 'LUCKNOW'?

NDA 2021 Solution View → 57

Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?

NDA 2021 Solution View → 58

How many 5-digit prime numbers can be formed using the digits 1,2,3,4,5 if the repetition of digits is not allowed?

NDA 2021 Solution View → 59

If C(20, n+2)=C(20, n-2) , then what is n equal to?

NDA 2020 Solution View → 60

What is the number of ways in which the letters of the word 'ABLE' can be arranged so that the vowels occupy even places?

NDA 2020 Solution View → 61

What is the maximum number of points of intersection of 5 non-overlapping circles?

NDA 2020 Solution View → 62

What is the number of diagonals of an octagon?

NDA 2019 Solution View → 63

If P(n, r)=2520 and C (n, r)=21 , then what is the value of C (n+1, r+1) ?

NDA 2019 Solution View → 64

What is C (47,4)+ C (51,3)+ C (50,3)+ C (49,3)+ C (48,3)+ C (47,3) equal to?

NDA 2019 Solution View → 65

There are 10 points in a plane. No three of these points are in a straight line. What is the total number of straight lines which can be formed by joining the points?

NDA 2019 Solution View → 66

How many three-digit even numbers can be formed using the digits 1,2,3,4 and 5 when repetition of digits is not allowed ?

NDA 2019 Solution View → 67

From 6 programmers and 4 typists, an office wants to recruit 5 people. What is the number of ways this can be done so as to recruit at least one typist?

NDA 2019 Solution View → 68

If n ! has 17 zeros, then what is the value of n ?

NDA 2019 Solution View → 69

If C (20, n +2)= C (20, n -2) , then what is n equal to?

NDA 2019 Solution View → 70

Where A^ is the complement of A . Let x be the number of integers lying between 2999 and 8001 which have at least two digits equal. Then x is equal to

NDA 2018 Solution View → 71

The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is

NDA 2018 Solution View → 72

There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers?

NDA 2018 Solution View → 73

What is the sum of all three-digit numbers that can be formed using all the digits 3,4 and 5 , when repetition of digits is not allowed?

NDA 2018 Solution View → 74

Three dice having digits 1,2,3,4,5 and 6 on their faces are marked I, II and III and rolled. Let x, y and z represent the number on die = I die = II and die -III respectively. What

NDA 2018 Solution View → 75

How many numbers between 100 and 1000 can be formed with the digits 5,6,7,8,9 , if the repetition of digits is not allowed?

NDA 2018 Solution View → 76

What is the number of triangles that can be formed by choosing the vertices from a set of 12 points in a plane, seven of which lie on the same straight line?

NDA 2018 Solution View → 77

How many four-digit numbers divisible by 10 can be formed using 1,5,0,6,7 without repetition of digits?

NDA 2018 Solution View → 78

How many different permutations can be made out of the letters of the word 'PERMUTATION'?

NDA 2017 Solution View → 79

Three-digit numbers are formed from the digits 1,2 and 3 in such a way that the digits are not repeated. What is the sum of such three-digit numbers?

NDA 2017 Solution View → 80

Five sticks of length 1,3,5,7 and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can from a triangle?

NDA 2017 Solution View → 81

A tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men

NDA 2017 Solution View → 82

Let A= 1,2,3,4,5,6,7,8,9,10 . Then the number of subsets of A containing two or three elements is

NDA 2017 Solution View → 83

The number of different words (eight-letter words) ending and beginning with a consonant which can be made out of the letters of the word 'EQUATION' is

NDA 2017 Solution View → 84

What is ⁴⁷ C ₄+ ⁵¹ C ₃+ _ j =2 ^5 ^ 52- j C ₃ equal to?

NDA 2016 Solution View → 85

What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets?

NDA 2016 Solution View → 86

What is the number of four-digit decimal numbers ( 1) in which no digit is repeated?

NDA 2016 Solution View → 87

What is the number of different messages that can be represented by three 0's and two 1's?

NDA 2016 Solution View → 88

Out of 15 points in a plane, n points are in the same straight line. 445 triangles can be formed by joining these points. What is the value of n ?

NDA 2016 Solution View → 89

What is the number of odd integers between 1000 and 9999 with no digit repeated?

NDA 2016 Solution View → 90

A five-digit number divisible by 3 is to be formed using the digits 0,1,2,3 and 4 without repetition of digits. What is the number of ways this can be done?

NDA 2016 Solution View → 91

If different words are formed with all the letters of the word 'AGAIN' and are arranged alphabetically among themselves as in a dictionary, the word at the 50th place will be

NDA 2015 Solution View → 92

A polygon has 44 diagonals. The number of its sides is

NDA 2015 Solution View → 93

The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is

NDA 2015 Solution View → 94

The number of ways in which 3 holiday tickets can be given to 20 employees of an organization if each employee is eligible for any one or more of the tickets, is

NDA 2015 Solution View → 95

How many words can be formed using all the letters of the word ‘NATION’ so that all the three vowels should never come together?

NDA 2015 Solution View → 96

Let A= 1,2,3,4,5,6,7,8,9,10 . Then the number of subsets of A containing exactly two elements is

NDA 2015 Solution View → 97

The number of 3-digit even numbers that can be formed from the digits 0,1,2,3,4 and 5 , repetition of digits being not allowed, is

NDA 2015 Solution View → 98

What is the number of ways in which one can post 5 letters in 7 letter boxes?

NDA 2014 Solution View → 99

The probability that in a random arrangement of the letters of the word 'UNIVERSITY' the two I's do not come together is

NDA 2014 Solution View → 100

Out of 7 consonants and 4 vowels, words are to be formed by involving 3 consonants and 2 vowels. The number of such words formed is:

NDA 2014 Solution View → 101

How many different words can be formed by taking four letters out of the letters of the word 'AGAIN' if each word has to start with A?

NDA 2014 Solution View → 102

Paragraph: Given that C(n, r): C(n, r+1)=1: 2 and C(n, r+1): C(n, r+2)=2: 3 . Question: What is r equal to?

NDA 2014 Solution View → 103

Paragraph: Given that C(n, r): C(n, r+1)=1: 2 and C(n, r+1): C(n, r+2)=2: 3 . Question: What is n equal to?

NDA 2014 Solution View → 104

Paragraph: Given that C(n, r): C(n, r+1)=1: 2 and C(n, r+1): C(n, r+2)=2: 3 . Question: What is P (n, r): C (n, r) equal to?

NDA 2014 Solution View → 105

What is the number of ways that a cricket team of 11 players can be made out of 15 players?

NDA 2014 Solution View → 106

If C (28,2 r)= C (28,2 r-4) , then what is r equal to?

NDA 2013 Solution View → 107

If P (77,31)=x and C (77,31)=y , then which one of the following is correct?

NDA 2013 Solution View → 108

In how many ways can the letters of the word 'GLOOMY' be arranged so that the two O's should not be together?

NDA 2013 Solution View → 109

What is the number of diagonals which can be drawn by joining the angular points of a polygon of 100 sides?

NDA 2012 Solution View → 110

What is the number of ways that 4 boys and 3 girls can be seated so that boys and girls alternate?

NDA 2012 Solution View → 111

The number of permutations that can be formed from all the letters of the word 'BASEBALL' is :

NDA 2012 Solution View → 112

What is the value of _ r=1 ^n P (n, r) r! ?

NDA 2011 Solution View → 113

There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. What is the number of ways in which the votes can be given?

NDA 2011 Solution View → 114

How many diagonals will be there in an n -sided regular polygon?

NDA 2011 Solution View → 115

In how many ways can 6 girls be seated in 2 empty chairs?

NDA 2011 Solution View → 116

A, B, C, D and E are coplanar points and three of them lie in a straight line. What is the maximum number of triangles that can be drawn with these points as their vertices?

NDA 2011 Solution View → 117

What is the value of n , if P(15, n-1): P(16, n-2)=3: 4 ?

NDA 2011 Solution View → 118

5 books are to be chosen from a lot of 10 books. If m is the number of ways of choice when one specified book is always included and n is the number of ways of choice when a specif

NDA 2011 Solution View → 119

What is the total number of combinations of n different things taken 1,2,3, , n at a time?

NDA 2011 Solution View → 120

Using the digits 1,2,3,4 and 5 only once, how many numbers greater than 41000 can be formed?

NDA 2011 Solution View →
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