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Mathematics - Continuity and Differentiability

Practise 20 NEST (NISER) previous year questions on Continuity and Differentiability, compiled from papers spanning 2011 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 NEST (NISER) tests.

Continuity and Differentiability has been asked in 13 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 20 questions in all. 0% of them were easy, 85% moderate and 15% tough. Most of its questions came from 2022, with 3 questions that year. In the last three years (2024–2026) it had 3 questions across 4 papers, about 0.8 per paper.

The chapter's 2 topics are not weighted equally: Continuity (11 questions, 55%) and Differentiability (9 questions, 45%) have been asked the most. Over the last five years the most frequent topics have been Differentiability (5) and Continuity (3). Differentiability has produced the most tough questions (2).

  1. 1Let be a function defined by Then2026Continuity
  2. 2Let be defined by . Then is2025Differentiability
  3. 3Let and be the function defined by If is differentiable and is continuous on , then2024 (Session 2)Continuity
  4. 4Define Let be the function defined by . Then the number of discontinuities of is2023 (Session 1)Continuity
  5. 5Let be a continuous function such that and and let be the function defined by for all . Then the value of is2023 (Session 1)Differentiability
  6. 6Let be a function satisfying for all .2022 (Session 1)Differentiability
  7. 7Let be defined by , where is the minimum of and . Then is2022 (Session 2)Differentiability
  8. 8Suppose is a real number and is defined as Then2022 (Session 2)Differentiability
  9. 9The function is defined as follows2021 (Session 2)Continuity
  10. 10Let be a function such that for all . Then2020 (Session 1)Differentiability
  11. 11Let be defined by . Here, is the greatest integer function for and is the positive square root of for . Then2020 (Session 2)Continuity
  12. 12Let be a continuous function. For an , suppose that where . Then2020 (Session 2)Differentiability
  13. 13Let be the function given by Then2019 (Session 2)Differentiability
  14. 14Let be a continuous function such that for any and . Then2019 (Session 2)Continuity
  15. 15Let be such that where is a positive integer. Suppose is continuous at . Then2018Continuity
  16. 16Let the function be defined as where for any real number denotes the greatest integer not exceeding . Then is continuous at2017Continuity
  17. 17Let . Let be a function defined as Then is2017Continuity
  18. 18Let a function be defined as follows. where and are real numbers with and . Then2016Continuity
  19. 19Define a function Then is2015Continuity
  20. 20Which of the following function is differentiable everywhere?2011Differentiability

Frequently Asked Questions

1.How many questions are available for Continuity and Differentiability?

This chapter includes 20 questions compiled from NEST (NISER) papers spanning 2011 to 2026.

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

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

3.Is Continuity and Differentiability an important chapter for NEST (NISER) Mathematics?

Continuity and Differentiability has appeared in 13 of the 16 years of NEST (NISER) papers covered here, with 20 questions across 15 papers - about one per paper it appears in.

4.What is the difficulty level of Continuity and Differentiability questions in NEST (NISER)?

Of the 20 questions analysed for this chapter, 0% are easy, 85% moderate and 15% tough. 2022 had the most, with 3 questions.

5.Which topics in Continuity and Differentiability should I focus on?

These topics have carried the most weightage in Continuity and Differentiability:

  • Continuity - 11 questions (55%)
  • Differentiability - 9 questions (45%)
  • Differentiability has produced the most tough questions (2).
6.Is Continuity and Differentiability's weightage in NEST (NISER) going up or down?

Across all 15 papers analysed, Continuity and Differentiability has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.