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Mathematics - Continuity and Differentiability

Practise 94 NDA previous year questions on Continuity and Differentiability, compiled from papers spanning 2010 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 NDA tests.

Continuity and Differentiability has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 94 questions in all. 19% of them were easy, 79% moderate and 2% tough. Most of its questions came from 2016, with 13 questions that year. In the last three years (2024–2026) it had 13 questions across 5 papers, about 2.6 per paper.

The chapter's 2 topics are not weighted equally: Continuity (57 questions, 61%) and Differentiability (37 questions, 39%) have been asked the most. Continuity has also led over the last five years, with 11 questions. Differentiability has produced the most tough questions (2).

  1. 1If is differentiable at , then consider the following statements : I. is continuous at II. Which of the statements given above is/are correc2026 (Phase 1)Differentiability
  2. 2What is the derivative of with respect to , where ?2026 (Phase 1)Differentiability
  3. 3Passage: Let Given that is continuous for all but not differentiable at . Further is continuous at . Question: What is the value of ?2026 (Phase 1)Continuity
  4. 4Passage: Let Given that is continuous for all but not differentiable at . Further is continuous at . Question: What is the value of ?2026 (Phase 1)Continuity
  5. 5Passage: Let and for p(x)=f(x)g(x) p(x) x=0 p(x) x=0$. Select the answer using the code given below :2026 (Phase 1)Continuity
  6. 6Passage: Let and for q(x)=f g(x) q(x) x=0 q(x) x=0$. Select the answer using the code given below :2026 (Phase 1)Continuity
  7. 7Consider the following for the two (02) items that follow: Let _{x 0} f'(x)$ equal to?2025 (Phase 1)Differentiability
  8. 8Consider the following for the two (02) items that follow: Let x = -1 x = 1$. Which of the statements given above is/are correct?2025 (Phase 1)Continuity
  9. 9For the following two (02) items: Consider the function k$?2025 (Phase 2)Continuity
  10. 10For the following two (02) items: Let the function be defined on the interval . What is at equal to?2025 (Phase 2)Differentiability
  11. 11For the following two (02) items: Let the function be defined on the interval . Consider the following statements: I. The function is differ2025 (Phase 2)Differentiability
  12. 12Let and , where [.] is the greatest integer function. Let Consider the following statements: 1. is differentiable for all 2. is continuous a2024 (Phase 1)Differentiability
  13. 13Paragraph: Let . Question: Consider the following statements: A. is continuous at . B. is continuous at Which of the statements given above 2024 (Phase 2)Continuity
  14. 14Paragraph: Let and is continuous. Question: What is the value of ?2023 (Phase 1)Continuity
  15. 15Let and is continuous. Question: What is the value of ?2023 (Phase 1)Continuity
  16. 16Let be continuous at . What is the value of a ?2023 (Phase 2)Continuity
  17. 17Let be continuous at . What is the value of b?2023 (Phase 2)Continuity
  18. 18Let If the function is differentiable at , then what is the value of ?2023 (Phase 2)Differentiability
  19. 19Let where [.] is the greatest integer function. What is the derivative of with respect to at ?2022 (Phase 1)Differentiability
  20. 20If , then which one of the following is correct?2021 (Phase 1)Differentiability
  21. 21If the function is continuous, then what is the value of ?2021 (Phase 1)Continuity
  22. 22Let If exists, then what is the value of ?2021 (Phase 2)Continuity
  23. 23Consider the following statements in respect of : 1. is continuous at . 2. is differentiable at . Which of the above statements is/are corre2021 (Phase 2)Differentiability
  24. 24Consider the following statements in respect of the function 1. It is continuous at , if . 2. It is continuous at . Which of the above state2021 (Phase 2)Continuity
  25. 25Consider the following statements for : 1. The function is continuous at . 2. The function is differentiable at . Which of the above stateme2020Continuity
  26. 26If , where , is to be continuous at , then the value of the function at2020Continuity
  27. 27The value of k which makes continuous at , is2019 (Phase 1)Continuity
  28. 28Consider the following statements in respect of the function for and ; 1. exists 2. is continuous at Which of the above statements is/are co2019 (Phase 2)Continuity
  29. 29For what value of is the function2019 (Phase 2)Continuity
  30. 30If , then which one of the following is correct?2018 (Phase 1)Continuity
  31. 31Consider the function . What is equal to?2018 (Phase 1)Differentiability
  32. 32If is continuous at , then which one of the following is correct?2018 (Phase 1)Continuity
  33. 33Consider the function Which one of the following is correct in respect of the function?2018 (Phase 2)Continuity
  34. 34For the function , which of the following is not correct?2018 (Phase 2)Differentiability
  35. 35If , then what is equal to2018 (Phase 2)Differentiability
  36. 36Let and , where and . Then what is equal to?2018 (Phase 2)Differentiability
  37. 37, then what is equal to?2017 (Phase 1)Differentiability
  38. 38Let be defined as follows : Which one of the following statements is correct in respect of the above function?2017 (Phase 1)Continuity
  39. 39Suppose the function is differentiable for all . Then can be any element of the interval2017 (Phase 1)Differentiability
  40. 40A function is defined as follows: Which one of the following is correct in respect of the above function?2017 (Phase 2)Continuity
  41. 41Consider the following : 1. is continuous at 2. is discontinuous at 3. is continuous at Which of the above are correct?2017 (Phase 2)Continuity
  42. 42A function is defined in by Which one of the following is correct in respect of the derivative of the function, i.e., ?2017 (Phase 2)Differentiability
  43. 43Consider the following statements : 1. Derivative of may not exist at some point. 2. Derivative of may exist finitely at some point. 3. Deri2017 (Phase 2)Differentiability
  44. 44The left-hand derivative of at where k is an integer and is the greatest integer function, is2017 (Phase 2)Differentiability
  45. 45If , then on the interval which one of the following is correct?2017 (Phase 2)Continuity
  46. 46The set of all points, where the function is differentiable, is2017 (Phase 2)Differentiability
  47. 47If , then is2017 (Phase 2)Continuity
  48. 48Let be the greatest integer function. Then the function is discontinuous at2017 (Phase 2)Continuity
  49. 49Consider the function , where . Which one of the following statements is correct?2016 (Phase 1)Differentiability
  50. 50A function is defined as follows: Consider the following statements: 1. The function is continuous at . 2. The function is continuous at . W2016 (Phase 1)Continuity

Frequently Asked Questions

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

This chapter includes 94 questions compiled from NDA papers spanning 2010 to 2026.

2.Are these questions only from NDA, or from other exams too?

These are NDA 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 NDA Mathematics?

Continuity and Differentiability has appeared in 17 of the 17 years of NDA papers covered here, with 94 questions across 30 papers - about 3 per paper it appears in.

4.What is the difficulty level of Continuity and Differentiability questions in NDA?

Of the 94 questions analysed for this chapter, 19% are easy, 79% moderate and 2% tough. 2016 had the most, with 13 questions.

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

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

  • Continuity - 57 questions (61%)
  • Differentiability - 37 questions (39%)
  • Differentiability has produced the most tough questions (2).
6.Is Continuity and Differentiability's weightage in NDA going up or down?

Across all 30 papers analysed, Continuity and Differentiability has averaged about 3.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 2.6 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.