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Mathematics - Continuity and Differentiability

Practise 18 BITSAT previous year questions on Continuity and Differentiability, compiled from papers spanning 2010 to 2024. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty BITSAT tests.

Continuity and Differentiability has been asked in 9 of the 16 years of BITSAT papers analysed (2009–2024), with 17 questions in all. 47% of them were easy, 29% moderate and 24% tough. Most of its questions came from 2024, with 3 questions that year. In the last three years (2022–2024) it had 3 questions across 3 papers, about 1 per paper.

The chapter's 3 topics are not weighted equally: Continuity (8 questions, 47%), Differentiability (8 questions, 47%), and Both Continuity and Differentiability (1 question, 6%) have been asked the most. Continuity has also led over the last five years, with 2 questions. Differentiability has produced the most tough questions (3).

  1. 1If is the number of points where is not differentiable then2024 (Memory Based Paper 1)Differentiability
  2. 2If , then at is2024 (Memory Based Paper 2)Both Continuity and Differentiability
  3. 3Let be the function defined by2024 (Memory Based Paper 3)Continuity
  4. 4Let be the function defined by2020Continuity
  5. 5Let f x = x p sin 1 x , x 0 0 , x = 0 then f x is continuous but not differentiable at x = 0 , if2018Continuity
  6. 6If f x = e x , x 0 1 - x , x 0 , then2017Differentiability
  7. 7The value of f ( 0 ) , so that the function f x = 2 x - sin - 1 x 2 x + tan - 1 x is continuous at each point in its domain, is2017Continuity
  8. 8Consider the greatest integer function, defined by f ( x ) = [ x ] , 0 x 2 . Then2017Differentiability
  9. 9The number of points at which the function is discontinuous is:2016Continuity
  10. 10If then is2016Differentiability
  11. 11If a function is given by , then at2015Continuity
  12. 12Let be a function such that If is differentiable at , then which one of the following is incorrect?2015Continuity
  13. 13Let Then which one of the following is true?2014Differentiability
  14. 14Let If is continuous at2014Continuity
  15. 15If the function is continuous at and then the values of a and are2012Continuity
  16. 16The function \( {f}( {x})=( {x}-1) {| n {x}|}\) is at \( {x}=1\)2011Differentiability
  17. 17The value of \( | {array}{ccc}1 & 2 & 3 \\ -4 & 3 & 6 \\ 2 & -7 & 9 {array} |\) is2010Differentiability
  18. 18Let \(f(x)= { (e^x-1 )^2}{ ( {x}{a} ) (1+ {x}{4} )}\) for \(x 0\), and \(f(0)=12\). If \( {f}\) is continuous at \(x=0\), then the value of 2010Differentiability

Frequently Asked Questions

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

This chapter includes 18 questions compiled from BITSAT papers spanning 2010 to 2024.

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

These are BITSAT 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 BITSAT Mathematics?

Continuity and Differentiability has appeared in 10 of the 16 years of BITSAT papers covered here, with 18 questions across 12 papers - about 2 per paper it appears in.

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

Of the 17 questions analysed for this chapter, 47% are easy, 29% moderate and 24% tough. 2024 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 - 8 questions (47%)
  • Differentiability - 8 questions (47%)
  • Both Continuity and Differentiability - 1 question (6%)
  • Differentiability has produced the most tough questions (3).
6.Is Continuity and Differentiability's weightage in BITSAT going up or down?

Across all 12 papers analysed, Continuity and Differentiability has averaged about 1.5 questions per paper. In the last three years (2022–2024), that average has fallen, at about 1.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.