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Mathematics - Continuity and Differentiability

Practise 113 AP EAMCET previous year questions on Continuity and Differentiability, compiled from papers spanning 2001 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 AP EAMCET tests.

Continuity and Differentiability has been asked in 19 of the 24 years of AP EAMCET papers analysed (2001–2024), with 113 questions in all. 34% of them were easy, 55% moderate and 12% tough. Most of its questions came from 2023, with 20 questions that year. In the last three years (2022–2024) it had 45 questions across 28 papers, about 1.6 per paper.

The chapter's 3 topics are not weighted equally: Continuity (76 questions, 67%), Differentiability (36 questions, 32%), and Continuity and Differentiability (1 question, 1%) have been asked the most. Continuity has also led over the last five years, with 48 questions. Continuity has produced the most tough questions (12).

  1. 1If the function defined by is continuous at , then27 May, 2025 (M)Continuity
  2. 2If a real valued function is continuous at , then ([x] denotes the greatest integer function)26 May, 2025 (M)Continuity
  3. 3If a real valued function is continuous at , then26 May, 2025 (E)Continuity
  4. 4If is continuous at then24 May, 2025 (M)Continuity
  5. 5If a real valued function , is continuous at , then23 May, 2025 (E)Continuity
  6. 6If the function is continuous everywhere, then22 May, 2025 (M)Continuity
  7. 7Assertion (A) : If , then Reason (R) : If exist, then it is called derivative of at . Then22 May, 2025 (M)Differentiability
  8. 8Let be defined by where denotes the greatest integer less than or equal to . If is continuous at , then22 May, 2025 (E)Continuity and Differentiability
  9. 9If a real valued function is continuous at , then21 May, 2025 (M)Continuity
  10. 10Match the functions in Column I with their properties in Column II. In the following denotes the greatest integer less than or equal to x Co21 May, 2025 (M)Continuity
  11. 11Consider the following functions I) II) III) IV) Then on Lagrange's mean value theorem is applicable to the functions21 May, 2025 (M)Differentiability
  12. 12If and , then which one of the following is true?21 May, 2025 (E)Continuity
  13. 13If a function defined by is continuous at , then21 May, 2025 (E)Continuity
  14. 14If , is continuous at , then23 May, 2024 (M)Continuity
  15. 15If is differentiable , then23 May, 2024 (M)Continuity
  16. 16The function23 May, 2024 (M)Continuity
  17. 17Let then which of the following is true22 May, 2024 (M)Continuity
  18. 18The function is22 May, 2024 (M)Continuity
  19. 19If a real valued function and is a finite value, then22 May, 2024 (E)Continuity
  20. 20If the function is continuous at then21 May, 2024 (E)Continuity
  21. 21If a function is continuous at then20 May, 2024 (M)Continuity
  22. 22The values of and for which the function is continuous at are20 May, 2024 (E)Continuity
  23. 23If is differentiable , then20 May, 2024 (E)Differentiability
  24. 24In the interval , the function is20 May, 2024 (E)Differentiability
  25. 25The function is19 May, 2024 (E)Continuity
  26. 26If ; Which of the following is true?19 May, 2024 (E)Continuity
  27. 27Let for every real number of . then19 May, 2024 (E)Continuity
  28. 28is a real valued function. If and is continuous on then18 May, 2024 (M)Continuity
  29. 29If is a real valued function then18 May, 2024 (M)Differentiability
  30. 30If a function defined on is discontinuous at , then19 May, 2023 (M)Differentiability
  31. 31Let represents the greatest integer not exceeding , Then the number of discontinuous points of in is19 May, 2023 (M)Continuity
  32. 32Assertion (A): If is not continuous at , then it is not differentiable at Reason (R): If is differentiable at a point, then it is continuous19 May, 2023 (M)Differentiability
  33. 33If18 May, 2023 (M)Differentiability
  34. 34Let terms and If , then is discontinuous at the point18 May, 2023 (E)Continuity
  35. 35If is differentiable at every , then the area (in sq units) of the triangle formed by the line with the coordinate axes is18 May, 2023 (E)Differentiability
  36. 36Let represents the greatest integer not exceeding and . If the function is continuous at , then is discontinuous at17 May, 2023 (M)Continuity
  37. 37is differentiable on and . If , then17 May, 2023 (M)Differentiability
  38. 38Let be a differentiable function such that , and then17 May, 2023 (M)Differentiability
  39. 39Let Then at and are respectively17 May, 2023 (M)Continuity
  40. 40If a function defined by is continuous on , and , then17 May, 2023 (E)Continuity
  41. 41If and , then the number of points at which is not differentiable, is17 May, 2023 (E)Differentiability
  42. 42If a function defined by , is continuous at , then16 May, 2023 (E)Continuity
  43. 43Let represents the greatest integer not more than .Then the number of discontinuous points of in is16 May, 2023 (E)Continuity
  44. 44If is continuous at all real , then15 May, 2023 (M)Continuity
  45. 45Let be a real valued function. If is a constant for all and , then15 May, 2023 (M)Differentiability
  46. 46If defined by is continuous on , then15 May, 2023 (M)Continuity
  47. 47The function has discontinuous points at15 May, 2023 (E)Continuity
  48. 48If is continuous on , then15 May, 2023 (E)Continuity
  49. 49Let represents the greatest integer not more than . The discontinuous points of the function lies in the interval15 May, 2023 (E)Continuity
  50. 50Which of the following is differentiable at07 Jul, 2022 (M)Differentiability

Frequently Asked Questions

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

This chapter includes 113 questions compiled from AP EAMCET papers spanning 2001 to 2025.

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

These are AP EAMCET 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 AP EAMCET Mathematics?

Continuity and Differentiability has appeared in 20 of the 25 years of AP EAMCET papers covered here, with 113 questions across 74 papers - about 2 per paper it appears in.

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

Of the 113 questions analysed for this chapter, 34% are easy, 55% moderate and 12% tough. 2023 had the most, with 20 questions.

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

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

  • Continuity - 76 questions (67%)
  • Differentiability - 36 questions (32%)
  • Continuity and Differentiability - 1 question (1%)
  • Continuity has produced the most tough questions (12).
6.Is Continuity and Differentiability's weightage in AP EAMCET going up or down?

Across all 74 papers analysed, Continuity and Differentiability has averaged about 1.5 questions per paper. In the last three years (2022–2024), that average has stayed about the same, at about 1.6 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.