NDA · Mathematics · UPSC · 2016–2026

Permutations and Combinations — NDA Mathematics PYQs

86 questions from this chapter, asked in 11 NDA exams between 2016–2026.

86questions

11NDA exams

2016–2026years covered

Questions asked per year

20264 Qs 202511 Qs 202412 Qs 20238 Qs 202213 Qs 20218 Qs 20203 Qs 20197 Qs 20189 Qs 20174 Qs 20167 Qs

Practice questions

Q1MCQ2026

Answer Logic

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

(A)

10

(B)

15

(C)

20

(D)

25

Q2MCQ2026

Answer Logic

What is the greatest value of $r$ satisfying the inequality $^{15} C_{r + 1} > 2 \times^{15} C_{r}$ ?

(A)

2

(B)

3

(C)

4

(D)

5

Q3MCQ2026

Answer Logic

If $n =^{m} C_{2}$ , then what is $^{n} C_{2}$ equal to ?

(A)

^{m + 1} C_{4}

(B)

2 \times^{m + 1} C_{4}

(C)

3 \times^{m + 1} C_{4}

(D)

^{m + 2} C_{4}

Q4MCQ2026

Answer Logic

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

(A)

24

(B)

18

(C)

15

(D)

12

Q5MCQ2025

Answer Logic

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?

(A)

360

(B)

300

(C)

288

(D)

240

Q6MCQ2025

Answer Logic

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

(A)

6

(B)

7

(C)

8

(D)

10

Q7MCQ2025

Answer Logic

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

(A)

6

(B)

9

(C)

12

(D)

24

Q8MCQ2025

Answer Logic

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

(A)

3

(B)

5

(C)

6

(D)

9

Q9MCQ2025

Answer Logic

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

(A)

n

(B)

2 n

(C)

3 n

(D)

4 n

Q10MCQ2025

Answer Logic

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

(A)

20

(B)

22

(C)

41

(D)

42

Why practise Permutations and Combinations PYQs?

Permutations and Combinations has appeared in 11 NDA Mathematics exams we track between 2016–2026. UPSC examiners consistently reuse concepts and question patterns from this topic — practising its previous year questions is the most reliable way to know exactly what to expect in your exam.

Permutations and Combinations — NDA Mathematics PYQs

Questions asked per year

Practice questions

Why practise Permutations and Combinations PYQs?

Other Mathematics topics

Basic Maths

Quadratic Equations

Trigonometric Functions

Properties of Triangle

Height and Distance

Binomial Theorem

Sequence and Series

Complex Number

Basics of Coordinate Geometry

Straight Lines

Circles

Parabola and Ellipse

Hyperbola and Rectangular Hyperbola

Relation and Function

Inverse Trigonometric Functions

Matrices

Determinants

Methods of Differentiation

Limits

Continuity and Differentiability

Application of Derivatives

Indefinite Integration

Definite Integration

Area Under the Curve

Differential Equations

Vector Algebra

3-D Geometry

Probability

Statistics

Binary Numbers

Logarithm

Sets