Mathematics - Sequences and Series
Practise 20 NEST (NISER) previous year questions on Sequences and Series, 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.
Sequences and Series has been asked in 11 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 20 questions in all. 10% of them were easy, 60% moderate and 30% tough. Most of its questions came from 2020, with 4 questions that year. In the last three years (2024–2026) it had 2 questions across 4 papers, about 0.5 per paper.
The chapter's 4 topics are not weighted equally: Arithmetic Progression (11 questions, 55%), Geometric Progression (7 questions, 35%), and Means (1 question, 5%) have been asked the most. Arithmetic Progression has also led over the last five years, with 2 questions. Arithmetic Progression has produced the most tough questions (4).
- 1Consider the closed interval and label it as . In the next step, divide the interval into three parts and delete the middle interval . Let b2024 (Session 1)Geometric Progression
- 2Let be the sum of all integers greater than 1000 and less than 2000 . If , then is2024 (Session 2)Arithmetic Progression
- 3Given a prime and an integer , let denote the largest integer such that divides . Define . Then2022 (Session 1)Geometric Progression
- 4Let be positive integers such that for , where is a constant. If , then is2022 (Session 2)Arithmetic Progression
- 5Let and be two sets of real numbers, where denotes the set of natural numbers. Define and . Then is equal to2021 (Session 1)Arithmetic Progression
- 6The number of positive integers such that is a perfect square is2021 (Session 2)Arithmetic Progression
- 7Let be all the positive divisors of . If , then equals2021 (Session 2)Arithmetic Progression
- 8For , let Define and for . Suppose is an even number greater than or equal to 2020. Then the least value of for which is2020 (Session 1)Geometric Progression
- 9If the roots of the equation are real, positive, distinct and in geometric progression then2020 (Session 2)Geometric Progression
- 10For a finite sequence of integers (where ), define2020 (Session 2)Arithmetic Progression
- 11Suppose are distinct integers chosen from . Let The value of for which takes maximum value is2020 (Session 2)Inequalities
- 12A positive integer is perfect if the sum of its positive divisors equals . If is a perfect number, then the sum of the reciprocal of its pos2019 (Session 1)Arithmetic Progression
- 13Let be the sum of digits of a positive integer . Then the number of solutions of the equation with is2019 (Session 2)Arithmetic Progression
- 14Let and define for all integers . Then is2018Arithmetic Progression
- 15If for some positive integer , we have , then is2017Geometric Progression
- 16Let be a positive integer. Suppose, between two distinct positive real numbers and arithmetic means and harmonic means are inserted. For and2017Arithmetic Progression
- 17Let be the arithmetic mean, geometric mean and harmonic mean respectively of two distinct positive real numbers. The roots of the quadratic 2016Means
- 18The set , and for all coincides with the set2014Geometric Progression
- 19For with , the value of is2012Geometric Progression
- 20Let be a sequence of numbers satisfying the relation for all and . Then is2011Arithmetic Progression
Frequently Asked Questions
1.How many questions are available for Sequences and Series?
This chapter includes 20 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 Sequences and Series chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.
3.Is Sequences and Series an important chapter for NEST (NISER) Mathematics?
Sequences and Series has appeared in 11 of the 16 years of NEST (NISER) papers covered here, with 20 questions across 16 papers - about one per paper it appears in.
4.What is the difficulty level of Sequences and Series questions in NEST (NISER)?
Of the 20 questions analysed for this chapter, 10% are easy, 60% moderate and 30% tough. 2020 had the most, with 4 questions.
5.Which topics in Sequences and Series should I focus on?
These topics have carried the most weightage in Sequences and Series:
- Arithmetic Progression - 11 questions (55%)
- Geometric Progression - 7 questions (35%)
- Means - 1 question (5%)
- Arithmetic Progression has produced the most tough questions (4).
6.Is Sequences and Series's weightage in NEST (NISER) going up or down?
Across all 16 papers analysed, Sequences and Series has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.5 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.