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Mathematics - Permutation Combination

Practise 18 NEST (NISER) previous year questions on Permutation Combination, compiled from papers spanning 2011 to 2024. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NEST (NISER) tests.

Permutation Combination has been asked in 8 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 18 questions in all. 0% of them were easy, 56% moderate and 44% tough. Most of its questions came from 2023, with 5 questions that year. In the last three years (2024–2026) it had 1 question across 4 papers, about 0.3 per paper.

The chapter's 4 topics are not weighted equally: Combination (9 questions, 50%), Permutation (6 questions, 33%), and Division of Identical items (2 questions, 11%) have been asked the most. Combination has also led over the last five years, with 4 questions. Permutation has produced the most tough questions (4).

  1. 1Let be the total number of integer solutions to the equation where each , is non-negative and not divisible by 3 . Then is equal to2024 (Session 1)Division of Identical items
  2. 2Let be the set of all natural numbers such that (i) , (ii) 0 appears at least once as a digit in the decimal expansion of , and (iii) the su2023 (Session 1)Combination
  3. 3Let be an integer. Let be points in the plane, which are the vertices of a regular -gon. The number of obtuse-angled triangles with vertices2023 (Session 1)Combination
  4. 4Let be the set of all 4-digit natural numbers with the following properties: (i) every digit of any element of belongs to the set , (ii) eve2023 (Session 2)Permutation
  5. 5Let be the number of integers such that (i) where are non-negative integers , and (ii) is neither a square nor a cube of a natural number. T2023 (Session 2)Combination
  6. 6Let be the number of solutions of the equation with and taking non-negative integer values. Then2023 (Session 2)Division of Identical items
  7. 7The number of arrangements of the letters of the word "PARALLEL" such that the letters P and R are together is2022 (Session 1)Permutation
  8. 8Three people are to be selected for one post of principal and two posts of vice-principal from the 6 candidates called for an interview. All2022 (Session 2)Combination
  9. 9Ameeya has 25 cards, each having a different integer from 1 to 25 printed on it. He wishes to place cards in a single row so that the number2021 (Session 1)Permutation
  10. 10Let be the set of all 6 -digit numbers, where all the digits of each number are from the set , and any digit that appears in any one of the 2021 (Session 1)Permutation
  11. 11Three different numbers are chosen at random from and arranged in increasing order . The probability that the resulting sequence is in arith2021 (Session 1)Combination
  12. 12NISER and CEBS anticipate admission of 200 students in the next semester and plans to offer jointly a number of online courses in both the p2021 (Session 2)Combination
  13. 13Let be a randomly chosen integer from the set . The probability that the sum of the digits of is equal to 24 is2020 (Session 2)Combination
  14. 14The number of positive divisors of the number 79200 which are not divisible by 4 is2020 (Session 2)Selection of one or more item
  15. 15Let be an integer and . Define and for any . Then2019 (Session 1)Permutation
  16. 16The number of ways of choosing 2 boys and 2 girls in a class for a game of mixed doubles is 1620 . Then, the number of ways of choosing 2 st2012Combination
  17. 17Let . If a student selects a function randomly from the set of all functions from onto , then what is the probability that the selected func2011Permutation
  18. 18The number of non-congruent triangles with sides of length where belong to ; so that the 3 digit number lies between 200 and 300 , is2011Combination

Frequently Asked Questions

1.How many questions are available for Permutation Combination?

This chapter includes 18 questions compiled from NEST (NISER) papers spanning 2011 to 2024.

2.Are these questions only from NEST (NISER), or from other exams too?

These are NEST (NISER) 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 NEST (NISER) Mathematics?

Permutation Combination has appeared in 8 of the 16 years of NEST (NISER) papers covered here, with 18 questions across 11 papers - about 2 per paper it appears in.

4.What is the difficulty level of Permutation Combination questions in NEST (NISER)?

Of the 18 questions analysed for this chapter, 0% are easy, 56% moderate and 44% tough. 2023 had the most, with 5 questions.

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

These topics have carried the most weightage in Permutation Combination:

  • Combination - 9 questions (50%)
  • Permutation - 6 questions (33%)
  • Division of Identical items - 2 questions (11%)
  • Permutation has produced the most tough questions (4).
6.Is Permutation Combination's weightage in NEST (NISER) going up or down?

Across all 11 papers analysed, Permutation Combination has averaged about 1.6 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.