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Mathematics - Continuity and Differentiability

Practise 7 IAT (IISER) previous year questions on Continuity and Differentiability, compiled from papers spanning 2017 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 IAT (IISER) tests.

Continuity and Differentiability has been asked in 5 of the 9 years of IAT (IISER) papers analysed (2017–2026), with 7 questions in all. 0% of them were easy, 71% moderate and 29% tough. Most of its questions came from 2026, with 2 questions that year. In the last three years (2023–2026) it had 4 questions across 3 papers, about 1.3 per paper.

The chapter's 2 topics are not weighted equally: Differentiability (4 questions, 57%) and Continuity (3 questions, 43%) have been asked the most. Over the last five years the most frequent topics have been Continuity (3) and Differentiability (2). Differentiability has produced the most tough questions (1).

  1. 1For real numbers and , consider the function given by How many pairs are there for which is continuous at every point of ?2026Continuity
  2. 2Let be the function given by . What is the number of points where is NOT differentiable?2026Differentiability
  3. 3Let be defined as , where denotes the greatest integer less than or equal to . Which one of the following statements is TRUE?2025Continuity
  4. 4Let be functions. If is continuous, then which one of the following cases implies that is continuous ?2024Continuity
  5. 5Which one of the following functions is differentiable at ?2023Differentiability
  6. 6Consider the function defined by Then, which of the following statements is correct?2021Differentiability
  7. 7Let be a differentiable function such that and for all . Which of the following is true?2017Differentiability

Frequently Asked Questions

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

This chapter includes 7 questions compiled from IAT (IISER) papers spanning 2017 to 2026.

2.Are these questions only from IAT (IISER), or from other exams too?

These are IAT (IISER) 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 IAT (IISER) Mathematics?

Continuity and Differentiability has appeared in 6 of the 10 years of IAT (IISER) papers covered here, with 7 questions across 6 papers - about one per paper it appears in.

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

Of the 7 questions analysed for this chapter, 0% are easy, 71% moderate and 29% tough. 2026 had the most, with 2 questions.

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

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

  • Differentiability - 4 questions (57%)
  • Continuity - 3 questions (43%)
  • Differentiability has produced the most tough questions (1).
6.Is Continuity and Differentiability's weightage in IAT (IISER) going up or down?

Across all 6 papers analysed, Continuity and Differentiability has averaged about 1.2 questions per paper. In the last three years (2023–2026), that average has stayed about the same, at about 1.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.