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Mathematics - Basic of Mathematics

Practise 18 NEST (NISER) previous year questions on Basic of Mathematics, compiled from papers spanning 2012 to 2025. 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.

Basic of Mathematics has been asked in 9 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 18 questions in all. 11% of them were easy, 72% moderate and 17% tough. Most of its questions came from 2021, with 3 questions that year. In the last three years (2024–2026) it had 4 questions across 4 papers, about 1 per paper.

The chapter's 3 topics are not weighted equally: Inequalities (8 questions, 44%), Divisibility Test (7 questions, 39%), and Logarithm (3 questions, 17%) have been asked the most. Inequalities has also led over the last five years, with 3 questions. Logarithm has produced the most tough questions (2).

  1. 1Let be the equivalence relation on defined by for if is a rational number. Then2025Logarithm
  2. 2Let be the set of integers such that and can be written as , with . Then the number of elements in is2025Inequalities
  3. 3The number of pairs of rational numbers such that is2024 (Session 1)Inequalities
  4. 4The greatest common divisor of and , where is any natural number greater than 3 , is equal to2024 (Session 2)Divisibility Test
  5. 5Let . Then the number of elements in is2022 (Session 1)Divisibility Test
  6. 6Let Then2022 (Session 2)Inequalities
  7. 7A pair of positive integers is said to be a happy pair if is a perfect square. Suppose is a positive integer such that is a happy pair. Then2021 (Session 1)Divisibility Test
  8. 8Let be real numbers each greater than 1 and let If , then must equal2021 (Session 1)Logarithm
  9. 9Let be the MÅ‘bius function defined for positive integers by Let be positive integers . Then2021 (Session 1)Divisibility Test
  10. 10For , a two digit number is defined for . A two digit number is called a special prime if both and are primes. Then the total number of spec2020 (Session 1)Divisibility Test
  11. 11If , then2020 (Session 2)Inequalities
  12. 12If are positive real numbers such that and , then equals2019 (Session 1)Inequalities
  13. 13The number of two-digit positive integers divisible by both their digits is2019 (Session 2)Divisibility Test
  14. 14For a positive integer , let denote the sum of positive divisors of and denote the number of elements of the set with , and define . Let be 2019 (Session 2)Logarithm
  15. 15For three arbitrary real numbers the mathematical identity is2015Inequalities
  16. 16Let and be distinct primes. Then the number of positive integer solutions of the equation is2015Divisibility Test
  17. 17For any real number denotes the largest integer less than or equal to and . The number of real solutions of is2014Inequalities
  18. 18For any real number , let denote the largest integer less than or equal to and . If are real numbers, then which of the following statements2012Inequalities

Frequently Asked Questions

1.How many questions are available for Basic of Mathematics?

This chapter includes 18 questions compiled from NEST (NISER) papers spanning 2012 to 2025.

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

These are NEST (NISER) questions specifically for the Basic of Mathematics chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Basic of Mathematics an important chapter for NEST (NISER) Mathematics?

Basic of Mathematics has appeared in 9 of the 16 years of NEST (NISER) papers covered here, with 18 questions across 13 papers - about one per paper it appears in.

4.What is the difficulty level of Basic of Mathematics questions in NEST (NISER)?

Of the 18 questions analysed for this chapter, 11% are easy, 72% moderate and 17% tough. 2021 had the most, with 3 questions.

5.Which topics in Basic of Mathematics should I focus on?

These topics have carried the most weightage in Basic of Mathematics:

  • Inequalities - 8 questions (44%)
  • Divisibility Test - 7 questions (39%)
  • Logarithm - 3 questions (17%)
  • Logarithm has produced the most tough questions (2).
6.Is Basic of Mathematics's weightage in NEST (NISER) going up or down?

Across all 13 papers analysed, Basic of Mathematics has averaged about 1.4 questions per paper. In the last three years (2024–2026), that average has fallen, at about 1.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.