Jump to a section

Mathematics - Continuity and Differentiability

Practise 22 JEE Advanced previous year questions on Continuity and Differentiability, compiled from papers spanning 2006 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 JEE Advanced tests.

Continuity and Differentiability has been asked in 14 of the 27 years of JEE Advanced papers analysed (2000–2026), with 22 questions in all. 14% of them were easy, 41% moderate and 45% tough. Most of its questions came from 2026, with 3 questions that year. In the last three years (2024–2026) it had 3 questions across 6 papers, about 0.5 per paper.

The chapter's 2 topics are not weighted equally: Differentiability (14 questions, 64%) and Continuity (8 questions, 36%) have been asked the most. Over the last five years the most frequent topics have been Continuity (4). Differentiability has produced the most tough questions (6).

  1. 1Let denote the set of all real numbers. Let be an arbitrary function and let be the function defined by , for all . Then which of the follow2026 (Paper 1)Continuity
  2. 2Consider the function defined by , where is the greatest integer less than or equal to . Let be the total number of points in the interval a2026 (Paper 1)Continuity
  3. 3For a real number , let denote the greatest integer less than or equal to . For a finite set , let denote the number of elements in the set 2026 (Paper 2)Continuity
  4. 4Let f : 0 , 1 be the function defined as f x = 4 x x - 1 4 2 x - 1 2 , where [ x ] denotes the greatest integer less than or equal to x . Th2023 (Paper 2)Continuity
  5. 5Let the function f : R R be defined by f x = x 3 x 2 + x 1 sin x and let g : R R be an arbitrary function. Let f g : R R be the product func2020 (Paper 1)Differentiability
  6. 6Let the functions f : - 1 , 1 and g : - 1 , 1 - 1 , 1 be defined by f x = 2 x - 1 + 2 x + 1 g x = x - x , where x denotes the greatest integ2020 (Paper 2)Differentiability
  7. 7Let f : and g : be functions satisfying f x + y = f x + f y + f x f y and f x = x g x for all x , y . If lim x 0 g x = 1 , then which of the2020 (Paper 2)Differentiability
  8. 8Let f 1 : R R , f 2 - 2 , 2 R , f 3 : - 1 , e 2 - 2 R and f 4 : be functions defined by (i) f 1 x = sin 1 - e - x 2 (ii) f 2 ( x ) = sin x t2018 (Paper 2)Differentiability
  9. 9Let x be the greatest integer less than or equals to x . Then, at which of the following point(s) the function f x = x cos x + x is disconti2017 (Paper 1)Continuity
  10. 10Let a , b R and f : R R be defined by f x = a cos x 3 - x + b x sin x 3 + x . Then f is -2016 (Paper 2)Differentiability
  11. 11Let f : - 1 2 , 2 R and g : - 1 2 , 2 R be functions defined by f x = x 2 - 3 and g x = x f x + 4 x - 7 f x , where y denotes the greatest i2016 (Paper 2)Differentiability
  12. 12Let g : R R be a differentiable function with g 0 = 0 , g 0 = 0 and g 1 0 . Let f x = x | x | g x , x 0 0 , x = 0 and h x = e | x | for all 2015 (Paper 1)Differentiability
  13. 13Let f : a , b 1 , be a continuous function and let g : R R be defined as g x = 0 i f x a , a x f t d t i f a x b , a b f t d t i f x b . The2014 (Paper 1)Continuity
  14. 14Let f : R R and g : R R be respectively given by f x = x + 1 and g x = x 2 + 1 . Define h : R R by h x = max f x , g x i f x 0 min f x , g x2014 (Paper 1)Differentiability
  15. 15Let then is2012 (Paper 1)Continuity
  16. 16For every integer , let and be real numbers. Let function be given by for all integers . If is continuous, then which of the following hold 2012 (Paper 2)Continuity
  17. 17Let be a function such that . If is differentiable at , then2011 (Paper 1)Differentiability
  18. 18If , then2011 (Paper 2)Differentiability
  19. 19Let be a real-valued function defined on the interval , by . Then which of the following statement(s) is (are) true ?2010 (Paper 1)Differentiability
  20. 20Let and be real valued functions defined on interval such that is continuous, and . Statement . Statement .2008 (Paper 1)Differentiability
  21. 21In the following denotes the greatest integer less than or equal to . Match the functions in Column I with the properties Column II.2007 (Paper 1)Differentiability
  22. 22If , then2006Differentiability

Frequently Asked Questions

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

This chapter includes 22 questions compiled from JEE Advanced papers spanning 2006 to 2026.

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

These are JEE Advanced 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 JEE Advanced Mathematics?

Continuity and Differentiability has appeared in 14 of the 21 years of JEE Advanced papers covered here, with 22 questions across 18 papers - about one per paper it appears in.

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

Of the 22 questions analysed for this chapter, 14% are easy, 41% moderate and 45% tough. 2026 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:

  • Differentiability - 14 questions (64%)
  • Continuity - 8 questions (36%)
  • Differentiability has produced the most tough questions (6).
6.Is Continuity and Differentiability's weightage in JEE Advanced going up or down?

Across all 18 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 0.5 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.