Permutations and Combinations · Mathematics · NDA
MCQ (Single Correct Answer)
1
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 Paper 2
2
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 Paper 2
3
A polygon has 44 diagonals. The number of its sides is
NDA 2015 Paper 2
4
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 Paper 2
5
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 Paper 2
6
What is the number of odd integers between 1000 and 9999 with no digit repeated?
NDA 2016 Paper 2
7
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 Paper 2
8
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 Paper 2
9
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 Paper 1
10
What is the number of four-digit decimal numbers (< 1) in which no digit is repeated?
NDA 2016 Paper 1
11
What is the number of different messages that can be represented by three 0's and two 1's?
NDA 2016 Paper 1
12
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 on the other side. The number of ways they can be seated is
NDA 2017 Paper 2
13
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 Paper 1
14
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 Paper 1
15
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 Paper 1
16
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 Paper 2
17
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 Paper 2
18
The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is
NDA 2018 Paper 2
19
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 Paper 1
20
How many four digit numbers divisible by 10 can be formed using 1, 5, 0, 6, 7 without repetition of digits?
NDA 2018 Paper 1
21
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 Paper 1
22
What is C(n, r) + 2C(n, r $$-$$ 1) + C(n, r $$-$$ 2) equal to?
NDA 2018 Paper 1
23
What is C(47, 4) + C(51, 3) + C(50, 3) + C(49, 3) + C(48, 3) + C(47, 3) equal to?
NDA 2019 Paper 2
24
If n! has 17 zeroes, then what is the value of n?
NDA 2019 Paper 2
25
What is the number of diagonals of an octagon?
NDA 2019 Paper 2
26
If P(n, r) = 2520 and C(n, r) = 21, then what is the value of C(n + 1, r + 1)?
NDA 2019 Paper 2
27
If C(20, n + 2) = C(20, n $$-$$2), then what is n equal to?
NDA 2019 Paper 1
28
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 Paper 1
29
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 Paper 1
30
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 Paper 1
31
What is the sum of all four-digit numbers formed by using all digits 0, 1, 4, 5 without repetition of digits?
NDA Mathematics 21 April 2024
32
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 relatives and 3 of them are his wife's relatives?
NDA Mathematics 21 April 2024
33
A triangle $PQR$ is such that 3 points lie on the side $PQ$, 4 points on $QR$ and 5 points on $RP$ respectively. Triangles are constructed using these points as vertices. What is the number of triangles so formed?
NDA Mathematics 21 April 2024
34
If $26! = n8^k$, where $k$ and $n$ are positive integers, then what is the maximum value of $k$?
NDA Mathematics 21 April 2024
35
How many four-digit natural numbers are there such that all of the digits are even?
NDA Mathematics 21 April 2024
36
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 Mathematics 21 April 2024
37
What is the number of different matrices, each having 4 entries that can be formed using 1, 2, 3, 4 (repetition is allowed)?
NDA Mathematics 21 April 2024
38
If 1! + 3! + 5! + 7! + ... + 199! is divided by 24, what is the remainder?
NDA Mathematics 3 September 2023
39
What is the maximum number of points of intersection of 10 circles?
NDA Mathematics 3 September 2023
40
If H is the Harmonic Mean of three numbers 10C4, 10C5, and 10C6, then what is the value of $\frac{270}{H}$ ?
NDA Mathematics 3 September 2023
41
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 Mathematics 16 April 2023
42
Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
NDA Mathematics 16 April 2023
43
m parallel lines cut n parallel lines giving rise to 60 parallelograms. What is the value of (m + n) ?
NDA Mathematics 16 April 2023
44
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 Mathematics 16 April 2023
45
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 Mathematics 16 April 2023
46
If the sum S is divided by 8, what is the remainder ?
NDA Mathematics 16 April 2023
47
If the sum S is divided by 60, what is the remainder ?
NDA Mathematics 16 April 2023
48
How many four-digit natural numbers are there such that all of the digits are odd ?
NDA Mathematics 4 September 2022
49
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 word that starts with C ?
NDA Mathematics 4 September 2022
50
How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed ?
NDA Mathematics 4 September 2022
51
How many 8-letter words with or without meaning, can be formed such that consonants and vowels occupy alternate positions?
NDA Mathematics 4 September 2022
52
How many 8-letter words with or without meaning, can be formed so that all consonants are together?
NDA Mathematics 4 September 2022
53
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 Mathematics 4 September 2022
54
If C(3n, 2n) = C(3n, 2n - 7), then what is the value of C(n, n - 5)?
NDA Mathematics 10 April 2022
55
How many odd numbers between 300 and 400 are there in which none of the digits is repeated ?
NDA Mathematics 10 April 2022
56
How many permutations are there of the letters of the word 'TIGER' in which the vowels should not occupy the even positions ?
NDA Mathematics 10 April 2022
57
What is the maximum value of n such that 5n divides (30! + 35!), where n is a natural number?
NDA Mathematics 10 April 2022
58
What is the value of 2(2 × 1) + 3(3 × 2 × 1) + 4(4 × 3 × 2 × 1) + 5(5 × 4 × 3 × 2 × 1) + .................. + 9(9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) + 2 ?
NDA Mathematics 10 April 2022
59
Consider the following statements:
1. $\frac{n!}{3!}$ is divisible by 6, where n > 3
2. $\frac{n!}{3!}+3 $ is divisible by 7, where n > 3
Which of the above statements is/are correct?
NDA Mathematics 10 April 2022
60
In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players ?
NDA Mathematics 10 April 2022
61
What is C(n, 1) + C(n, 2) + _ _ _ _ _ + C(n, n) equal to
NDA Mathematics 18 April 2021
62
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 Mathematics 18 April 2021
63
In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?
NDA Mathematics 18 April 2021