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Mathematics - Continuity and Differentiability

Practise 27 KCET 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 KCET tests.

Continuity and Differentiability has been asked in 18 of the 20 years of KCET papers analysed (2007–2026), with 27 questions in all. 56% of them were easy, 41% moderate and 4% tough. Most of its questions came from 2025, with 3 questions that year. In the last three years (2024–2026) it had 5 questions across 3 papers, about 1.7 per paper.

The chapter's 2 topics are not weighted equally: Continuity (22 questions, 81%) and Differentiability (5 questions, 19%) have been asked the most. Continuity has also led over the last five years, with 5 questions. Continuity has produced the most tough questions (1).

  1. 1If is continuous at , then2026Continuity
  2. 2Match the following: In the following, denotes the greatest integer less than or equal to x . {array}{|l|l|l|l|} & {Column - I} & & {Column 2025Continuity
  3. 3The function is differentiable at . Then2025Differentiability
  4. 4A function is2025Continuity
  5. 5The function is2024Continuity
  6. 6The function is discontinuous on every point of the set2023Continuity
  7. 7At , the function is2021Differentiability
  8. 8If , then2020Continuity
  9. 9Rolle's theorem is not applicable in which one of the following cases?2019Differentiability
  10. 10If \( f(x)= \{ {array}{cc} { 3 x}{e^{2 x}-1} & x 0 \\ k-2 & x=0 {array} . \) is continuous at \( x=0 \), then \( k= \)2019Continuity
  11. 11If \[ f(x)= \{ {array}{cl} { {1+ {kx}}- {1- {kx}}}{ {x}} ; & { if }-1 {x} 0 \\ {2 {x}+1}{ {x}-1} ; & { if } 0 {x} 1 {array} . \] is continuo2018Continuity
  12. 12If \( f(x)= \{ {array}{cc} { _{e} x}{x-1} & ; x 1 \\ k & ; x=1 {array} . \) is continuous at \( x=1 \), then the value of \( k \) is2018Continuity
  13. 13The function \( f(x)=x^{2}+2 x-5 \) is strictly increasing in the interval2017Continuity
  14. 14The function \( f(x)=[x] \) where \( [x] \) the greatest integer function is continuous at2016Continuity
  15. 15The system of linear equations \( x+y+z=6, x+2 y+3 z=10 \) and \( x+2 y+a z=b \) has no solutions when2015Continuity
  16. 16The value of \( (1^{ } )+ (89^{ } ) \) is2015Differentiability
  17. 17If \( {A}= [ {array}{ll} & 2 \\ 2 & {array} ] \) and \( | {A}^{3} |=27 \), then \( = \)2015Continuity
  18. 18The value of the integral is2014Differentiability
  19. 19\( { 2 x}{ ( ^{2} x+2 ^{2} x .} d x= \)2014Continuity
  20. 20If , then is2013Continuity
  21. 21If . Then, which of the following is true?2013Continuity
  22. 22If is continuous at , then the value of is2012Continuity
  23. 23is continuous at , then the value of is2011Continuity
  24. 24The function , where denotes the greatest integer not greater than , is2010Continuity
  25. 25The function is2010Continuity
  26. 26Then, which of the following is true ?2008Continuity
  27. 27If the function continuous at , then the value of is2007Continuity

Frequently Asked Questions

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

This chapter includes 27 questions compiled from KCET papers spanning 2007 to 2026.

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

These are KCET 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 KCET Mathematics?

Continuity and Differentiability has appeared in 18 of the 20 years of KCET papers covered here, with 27 questions across 18 papers - about 2 per paper it appears in.

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

Of the 27 questions analysed for this chapter, 56% are easy, 41% moderate and 4% tough. 2025 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 - 22 questions (81%)
  • Differentiability - 5 questions (19%)
  • Continuity has produced the most tough questions (1).
6.Is Continuity and Differentiability's weightage in KCET going up or down?

Across all 18 papers analysed, Continuity and Differentiability has averaged about 1.5 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.