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Mathematics - Continuity and Differentiability

Practise 108 MHTCET previous year questions on Continuity and Differentiability, compiled from papers spanning 2007 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 MHTCET tests.

Continuity and Differentiability has been asked in 16 of the 17 years of MHTCET papers analysed (2007–2026), with 108 questions in all. 27% of them were easy, 64% moderate and 9% tough. Most of its questions came from 2023, with 17 questions that year. In the last three years (2024–2026) it had 36 questions across 59 papers, about 0.6 per paper.

The chapter's 2 topics are not weighted equally: Continuity (100 questions, 93%) and Differentiability (8 questions, 7%) have been asked the most. Continuity has also led over the last five years, with 60 questions. Continuity has produced the most tough questions (9).

  1. 1Let denotes the greatest integer less than or equal to x and , then which of the following is true ?20 Apr, 2026 (M)Continuity
  2. 2If the function defined by is continuous at , then ..........20 Apr, 2026 (E)Continuity
  3. 3If the function , for is continuous at , then the value of is...19 Apr, 2026 (E)Continuity
  4. 4The number of point / points where the function is discontinuous is......18 Apr, 2026 (M)Continuity
  5. 5If for , is continuous at , then the value of is equal to18 Apr, 2026 (E)Continuity
  6. 6Which of the following function is discontinuous at ?17 Apr, 2026 (M)Continuity
  7. 7If the function for is continuous at , then the value of is equal to17 Apr, 2026 (E)Continuity
  8. 8If the derivative of the function is continuous everywhere then16 Apr, 2026 (M)Continuity
  9. 9If the function f is continuous at , where , for , then16 Apr, 2026 (E)Continuity
  10. 10If the function f is continuous at , where , for , then the value of is....15 Apr, 2026 (M)Continuity
  11. 11The value of f(0) so that the function , is continuous at , is15 Apr, 2026 (E)Continuity
  12. 12If is continuous at , then13 Apr, 2026 (M)Continuity
  13. 13If is continuous at , where , for and , then the value of is ...13 Apr, 2026 (E)Continuity
  14. 14Let the function be defined as: If is continuous at , then the value of is...11 Apr, 2026 (M)Continuity
  15. 15Let the function f be defined by , for and then f is11 Apr, 2026 (E)Continuity
  16. 16If is continuous at and , then the value of is27 Apr, 2025 (E)Continuity
  17. 17Let then is continuous on the set26 Apr, 2025 (E)Continuity
  18. 18The function is23 Apr, 2025 (E)Continuity
  19. 19If the function is continuous in then22 Apr, 2025 (M)Continuity
  20. 20If , is continuous at then20 Apr, 2025 (M)Continuity
  21. 21is continuous at , then where is greatest integer function20 Apr, 2025 (E)Continuity
  22. 22If is continuous at point where then the values of and b , respectively, are19 Apr, 2025 (M)Continuity
  23. 23Let . is continuous in , then is16 May, 2024 (M)Continuity
  24. 24If the function f defined on by is continuous, then k is equal to16 May, 2024 (E)Continuity
  25. 25If the function is continuous everywhere, then the values of A and B are respectively15 May, 2024 (E)Continuity
  26. 26If is continuous at , then11 May, 2024 (M)Continuity
  27. 27Let If is continuous at , then the value of a is11 May, 2024 (E)Continuity
  28. 28The values of and , so that the function is continuous for , are respectively given by10 May, 2024 (M)Continuity
  29. 29Let k be a non-zero real number. If is a continuous function, then the value of is09 May, 2024 (M)Continuity
  30. 30Let , for , where denotes the greatest integer function. Then the number of points of discontinuity of is equal to09 May, 2024 (E)Continuity
  31. 31Let . If the function is defined as is continuous in the interval , then an ordered pair is04 May, 2024 (M)Continuity
  32. 32If , for is continuous at , then04 May, 2024 (E)Continuity
  33. 33Let is continuous in , then is03 May, 2024 (M)Continuity
  34. 34If the function if . if . is continuous at , then03 May, 2024 (E)Continuity
  35. 35Let K be the set of all real values of , where the function is not differentiable. Then the set K is02 May, 2024 (M)Differentiability
  36. 36The value of , for which the function is continuous at , is02 May, 2024 (E)Continuity
  37. 37The function , where denotes the greatest integer function, is discontinuous at14 May, 2023 (M)Continuity
  38. 38The function defined on by is continuous at , then is14 May, 2023 (E)Continuity
  39. 39The function where is discontinuous at13 May, 2023 (M)Continuity
  40. 40If a continuous random variable has probability density function given by then a has the value13 May, 2023 (M)Continuity
  41. 41If is continuous on its domain , where then the value of is13 May, 2023 (E)Continuity
  42. 42The c.d.f. associated with p.d.f. is13 May, 2023 (E)Continuity
  43. 43The values of and , so that the function is continuous for , are respectively given by12 May, 2023 (M)Continuity
  44. 44Given If is continuous at , then value of is12 May, 2023 (E)Continuity
  45. 45If is continuous in the interval , then is equal to11 May, 2023 (M)Continuity
  46. 46Is continuous at , then the value of is11 May, 2023 (E)Continuity
  47. 47Let be a continuous function such that Let and be the area of the region bounded by and the -axis, then is11 May, 2023 (E)Continuity
  48. 48If the function is continuous in , then the value of is where10 May, 2023 (M)Continuity
  49. 49The value of for the function on if LMVT can be applied, is10 May, 2023 (E)Differentiability
  50. 50Let is not differentiable at , then is10 May, 2023 (E)Differentiability

Frequently Asked Questions

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

This chapter includes 108 questions compiled from MHTCET papers spanning 2007 to 2026.

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

These are MHTCET 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 MHTCET Mathematics?

Continuity and Differentiability has appeared in 16 of the 17 years of MHTCET papers covered here, with 108 questions across 91 papers - about one per paper it appears in.

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

Of the 108 questions analysed for this chapter, 27% are easy, 64% moderate and 9% tough. 2023 had the most, with 17 questions.

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

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

  • Continuity - 100 questions (93%)
  • Differentiability - 8 questions (7%)
  • Continuity has produced the most tough questions (9).
6.Is Continuity and Differentiability's weightage in MHTCET going up or down?

Across all 91 papers analysed, Continuity and Differentiability has averaged about 1.2 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.6 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.