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Mathematics - Permutation Combination

Practise 129 NDA previous year questions on Permutation Combination, compiled from papers spanning 2010 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NDA tests.

Permutation Combination has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 129 questions in all. 20% of them were easy, 77% moderate and 3% tough. Most of its questions came from 2024, with 12 questions that year. In the last three years (2024–2026) it had 30 questions across 5 papers, about 6 per paper.

The chapter's 8 topics are not weighted equally: Permutation (54 questions, 42%), Combination (53 questions, 41%), and Arrangement under Constraint (11 questions, 9%) have been asked the most. Permutation has also led over the last five years, with 21 questions. Permutation has produced the most tough questions (3).

  1. 1What is the maximum number of points of intersection of circles ?2026 (Phase 1)Combination
  2. 2If then what is equal to ?2026 (Phase 1)Combination
  3. 3How many numbers greater than can be formed using the digits , , and (repetition of digits is not allowed) ?2026 (Phase 1)Permutation
  4. 4Passage: A 4-digit number is selected at random formed by using the digits , , , and (where repetition of digits is not allowed). Question: 2026 (Phase 1)Arrangement under Constraint
  5. 5Passage: A 4-digit number is selected at random formed by using the digits , , , and (where repetition of digits is not allowed). Question: 2026 (Phase 1)Permutation
  6. 6Passage: A 4-digit number is selected at random formed by using the digits , , , and (where repetition of digits is not allowed). Question: 2026 (Phase 1)Permutation
  7. 7Passage: A 4-digit number is selected at random formed by using the digits , , , and (where repetition of digits is not allowed). Question: 2026 (Phase 1)Arrangement under Constraint
  8. 8How many 7-letter words (with or without meaning) can be constructed using all the letters of the word CAPITAL so that all consonants come t2025 (Phase 1)Arrangement under Constraint
  9. 9How many sides are there in a polygon which has 20 diagonals?2025 (Phase 1)Combination
  10. 10In how many ways can the letters of the word DELHI be arranged keeping the positions of vowels and consonants unchanged?2025 (Phase 1)Permutation
  11. 11What is the number of positive integer solutions of ?2025 (Phase 1)Division of Identical items
  12. 12If the number of selections of as well as things from different things are equal, then what is the value of ?2025 (Phase 1)Combination
  13. 13What is the number of selections of at most 3 things from 6 different things?2025 (Phase 1)Combination
  14. 14Let and . If , then what is the value of ?2025 (Phase 2)Factorial
  15. 15Let be a natural number. The number of consecutive zeros at the end of the expansion of is exactly 2. How many values of are possible?2025 (Phase 2)Exponent of prime
  16. 16How 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)?2025 (Phase 2)Permutation
  17. 17For 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 joi2025 (Phase 2)Combination
  18. 18For 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 b2025 (Phase 2)Combination
  19. 19What is the sum of all four digit numbers formed by using all digits without repetition of digits?2024 (Phase 1)Summation of Numbers
  20. 20A 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 and2024 (Phase 1)Combination
  21. 21A triangle PQR is such that 3 points lie on the side points on QR and 5 points on respectively. Triangles are constructed using these points2024 (Phase 1)Combination
  22. 22If , where and are positive integers, then what is the maximum value of ?2024 (Phase 1)Exponent of prime
  23. 23How many four-digit natural numbers are there such that all of the digits are even?2024 (Phase 1)Permutation
  24. 24Four digit numbers are formed by using the digits without repetition of digits. How many of them are divisible by 4 ?2024 (Phase 1)Permutation
  25. 25How many 4-digit numbers are there having all digits as odd?2024 (Phase 2)Permutation
  26. 26In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?2024 (Phase 2)Permutation
  27. 27The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements a2024 (Phase 2)Permutation
  28. 28In how many ways can a student choose courses out of courses if 2 courses are compulsory ?2024 (Phase 2)Combination
  29. 29The letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternativel2024 (Phase 2)Permutation
  30. 30Three perfect dice and are rolled. Let and represent the numbers on and respectively. What is the number of possible outcomes such that ?2024 (Phase 2)Combination
  31. 31What is the number of 6 digit numbers that can be formed only by using and 5 (each once); and divisible by 6 ?2023 (Phase 1)Permutation
  32. 32parallel lines cut parallel lines giving rise to 60 parallelograms. What is the value of ?2023 (Phase 1)Combination
  33. 33Let be the number of permutations of the word 'PERMUTATIONS' and be the number of permutations of the word 'COMBINATIONS'. Which one of the 2023 (Phase 1)Permutation
  34. 345 - digit numbers are formed using the digits without repetition. What is the percentage of numbers which are greater than 50,000 ?2023 (Phase 1)Permutation
  35. 35Paragraph: Consider the sum Question: If the sum S is divided by 8 , what is the remainder?2023 (Phase 1)Factorial
  36. 36What is the maximum number of points of intersection of 10 circles?2023 (Phase 2)Combination
  37. 37Three 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 s2023 (Phase 2)Permutation
  38. 38Three 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 sit2023 (Phase 2)Arrangement under Constraint
  39. 39If , then what is the value of ?2022 (Phase 1)Combination
  40. 40How many odd numbers between 300 and 400 are there in which none of the digits is repeated?2022 (Phase 1)Permutation
  41. 41How many permutations are there of the letters of the word 'TIGER' in which the vowels should not occupy the even positions?2022 (Phase 1)Arrangement under Constraint
  42. 42What is the maximum value of such that divides (30! +35 !), where is a natural number?2022 (Phase 1)Exponent of prime
  43. 43In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players?2022 (Phase 1)Combination
  44. 44How many four-digit natural numbers are there such that all of the digits are odd?2022 (Phase 2)Permutation
  45. 45If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) a2022 (Phase 2)Permutation
  46. 46Paragraph: Consider the word 'QUESTION' : Question: How many 4-letter words each of two vowels and two consonants with or without meaning, c2022 (Phase 2)Permutation
  47. 47Paragraph: Consider the word 'QUESTION' : Question: How many 8 -letter words with or without meaning, can be formed such that consonants and2022 (Phase 2)Permutation
  48. 48Paragraph: Consider the word 'QUESTION' : Question: How many 8 -letter words with or without meaning, can be formed so that all consonants a2022 (Phase 2)Permutation
  49. 49A 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 bl2022 (Phase 2)Combination
  50. 50In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?2021 (Phase 1)Combination

Frequently Asked Questions

1.How many questions are available for Permutation Combination?

This chapter includes 129 questions compiled from NDA papers spanning 2010 to 2026.

2.Are these questions only from NDA, or from other exams too?

These are NDA questions specifically for the Permutation Combination chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Permutation Combination an important chapter for NDA Mathematics?

Permutation Combination has appeared in 17 of the 17 years of NDA papers covered here, with 129 questions across 32 papers - about 4 per paper it appears in.

4.What is the difficulty level of Permutation Combination questions in NDA?

Of the 129 questions analysed for this chapter, 20% are easy, 77% moderate and 3% tough. 2024 had the most, with 12 questions.

5.Which topics in Permutation Combination should I focus on?

These topics have carried the most weightage in Permutation Combination:

  • Permutation - 54 questions (42%)
  • Combination - 53 questions (41%)
  • Arrangement under Constraint - 11 questions (9%)
  • Permutation has produced the most tough questions (3).
6.Is Permutation Combination's weightage in NDA going up or down?

Across all 32 papers analysed, Permutation Combination has averaged about 4.0 questions per paper. In the last three years (2024–2026), that average has risen, at about 6.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.