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Mathematics - Continuity and Differentiability

Practise 154 JEE Main previous year questions on Continuity and Differentiability, compiled from papers spanning 2002 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 Main tests.

Continuity and Differentiability has been asked in 23 of the 25 years of JEE Main papers analysed (2002–2026), with 154 questions in all. 21% of them were easy, 42% moderate and 37% tough. Most of its questions came from 2021, with 28 questions that year. In the last three years (2024–2026) it had 33 questions across 49 papers, about 0.7 per paper.

The chapter's 2 topics are not weighted equally: Differentiability (81 questions, 53%) and Continuity (73 questions, 47%) have been asked the most. Differentiability has also led over the last five years, with 35 questions. Differentiability has produced the most tough questions (34).

  1. 1For the function , , consider the following statements: Statement I: is differentiable for all . Statement II: is increasing in . In the lig08 Apr, 2026 (E)Differentiability
  2. 2Let . If is continuous at , then the value of is:08 Apr, 2026 (E)Continuity
  3. 3Let g f$ is discontinuous, is __________.06 Apr, 2026 (E)Continuity
  4. 4The number of points, at which the function , , is not differentiable, is _____.04 Apr, 2026 (M)Differentiability
  5. 5Let and . If the number of points where is not continuous and is not differentiable are and respectively, then is equal to ______04 Apr, 2026 (E)Continuity
  6. 6The number of points in the interval , at which the function , where denotes the greatest integer function, is discontinuous, is _______.02 Apr, 2026 (E)Continuity
  7. 7Let . Consider the following two statements : (I) is discontinous at . (II) is continous at . Then,28 Jan, 2026 (E)Continuity
  8. 8If the function is continuous at , then the value of is equal to24 Jan, 2026 (M)Continuity
  9. 9Let be such that the function x {R} 34( + )$ is equal to24 Jan, 2026 (M)Differentiability
  10. 10Let denote the greatest integer less than or equal to . If the function is continuous at , then is equal to24 Jan, 2026 (E)Continuity
  11. 11Let be continuous at . If , then is equal to:23 Jan, 2026 (M)Continuity
  12. 12If is continuous at , then is equal to23 Jan, 2026 (E)Continuity
  13. 13Let denote the greatest integer function, and let . Let : the function is discontinuous at . Then equals22 Jan, 2026 (E)Continuity
  14. 14The number of points of discontinuity of the function , where denotes the greatest integer function is ________07 Apr, 2025 (M)Continuity
  15. 15Let and be the number of points at which the function , is not differentiable and not continuous, respectively. Then is equal to ________ .04 Apr, 2025 (M)Differentiability
  16. 16Let be continuous at . Then is equal to03 Apr, 2025 (M)Continuity
  17. 17Let the function be not differentiable at the two points and . Then the distance of the point from the line is equal to :29 Jan, 2025 (E)Differentiability
  18. 18Let where [.] denotes greatest integer function. If and are the number of points, where f is not continuous and is not differentiable, respe28 Jan, 2025 (M)Differentiability
  19. 19Let denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function , is not continuous 24 Jan, 2025 (E)Differentiability
  20. 20If the function is continuous at , then is equal to23 Jan, 2025 (M)Continuity
  21. 21Let be a real differentiable function such that and for all . Then is equal to :22 Jan, 2025 (M)Differentiability
  22. 22Let the function, be differentiable for all , where . If the area of the region enclosed by and the line is , then the value of is ________22 Jan, 2025 (M)Differentiability
  23. 23Let be a function given by \( \{ {array}{cc} ( {8}{7} )^{ { 8 x}{ 7 x}}, & 0 where . If is continuous at , then is equal to09 Apr, 2024 (M)Continuity
  24. 24For , let be a continous function at . Then is equal to :08 Apr, 2024 (E)Continuity
  25. 25Let denote the greatest integer less than or equal to . Let be a function defined by . Let be the set of all points in the interval at which06 Apr, 2024 (E)Continuity
  26. 26If the function , is continuous at , then is equal to :05 Apr, 2024 (M)Continuity
  27. 27Let be given by , where denotes the greatest integer less than or equal to . The number of points, where is not continuous, is :05 Apr, 2024 (E)Continuity
  28. 28Let be a function given by where . If is continuous at , then is equal to :04 Apr, 2024 (M)Continuity
  29. 29If the function is continuous at , then the value of is equal to04 Apr, 2024 (E)Continuity
  30. 30Let f : R → R be defined as f x = a − b cos 2 x x 2 ; x 0 x 2 + c x + 2 ; 0 ≤ x ≤ 1 2 x + 1 ; x 1 If f is continuous everywhere in R and m i01 Feb, 2024 (M)Differentiability
  31. 31Let f x = 2 x 2 + 5 x - 3 , x ∈ R . If m and n denote the number of points where f is not continuous and not differentiable respectively, th01 Feb, 2024 (E)Differentiability
  32. 32Let g x be a linear function and f x = g x , x ≤ 0 1 + x 2 + x 1 x , x 0 , is continuous at x = 0 . If f ' 1 = f − 1 , then the value of g 331 Jan, 2024 (M)Differentiability
  33. 33Consider the function f : 0 , ∞ → R defined by f x = e − log e x . If m and n be respectively the number of points at which f is not continu31 Jan, 2024 (E)Differentiability
  34. 34If the function f x = 1 | x | , | x | ≥ 2 a x 2 + 2 b , | x | 2 is differentiable on R , then 48 ( a + b ) is equal to _______.30 Jan, 2024 (M)Differentiability
  35. 35Let a and b be real constants such that the function f defined by f x = x 2 + 3 x + a , x ≤ 1 b x + 2 , x 1 be differentiable on R . Then, t30 Jan, 2024 (E)Differentiability
  36. 36Let f : R - { 0 } → R be a function satisfying f x y = f ( x ) f ( y ) for all x , y , f ( y ) ≠ 0 . If f ' ( 1 ) = 2024 , then30 Jan, 2024 (E)Differentiability
  37. 37Let f x = lim r → x 2 r 2 ( f ( r ) ) 2 - f ( x ) f ( r ) r 2 - x 2 - r 3 e f ( r ) r be differentiable in ( - ∞ , 0 ) ∪ ( 0 , ∞ ) and f ( 129 Jan, 2024 (E)Differentiability
  38. 38Consider the function f x = a 7 x - 12 - x 2 b x 2 - 7 x + 12 , x 3 2 sin ( x - 3 ) x - [ x ] , x 3 b , x = 3 ,where [ x ] denotes the great27 Jan, 2024 (M)Continuity
  39. 39Consider the function f : ( 0 , 2 ) → R defined by f ( x ) = x 2 + 2 x and the function g ( x ) defined by g x = min { f ( t ) } , 0 t ≤ x a27 Jan, 2024 (E)Differentiability
  40. 40Let x denote the greatest integer function and f x = max 1 + x + x , 2 + x , x + 2 x , 0 x 2 , where f is not continuous and n be the number15 Apr, 2023 (M)Differentiability
  41. 41Let x be the greatest integer x . Then the number of points in the interval ( 2 , 1 ) where the function f x = x + x - x is discontinuous, i12 Apr, 2023 (M)Continuity
  42. 42Let f x = x 2 - x + - x + x , where x and t denotes the greatest integer less than or equal to t . Then, f is11 Apr, 2023 (M)Continuity
  43. 43Let f and g be two functions defined by f x = x + 1 , x 0 x - 1 , x 0 and g x = x + 1 , x 0 1 , x 0 .Then g o f x is11 Apr, 2023 (E)Differentiability
  44. 44Let f : - 2 , 2 be defined by f x = x x , - 2 x 0 x - 1 x , 0 x 2 where x denotes the greatest integer function. If m and n respectively are10 Apr, 2023 (M)Differentiability
  45. 45Let k and m be positive real numbers such that the function f x = 3 x 2 + k x + 1 , 0 x 1 m x 2 + k 2 , x 1 is differentiable for all x 0 . 08 Apr, 2023 (E)Differentiability
  46. 46Let a and t be the greatest integer t , then the number of points, where the function f x = a + 13 sin x , x 0 , is not differentiable, is _06 Apr, 2023 (M)Differentiability
  47. 47Suppose f is a function satisfying f ( x + y ) = f ( x ) + f ( y ) for all x , y and f ( 1 ) = 1 5 . If n = 1 m f ( n ) n ( n + 1 ) ( n + 2 29 Jan, 2023 (M)Differentiability
  48. 48Let f and g be twice differentiable functions on R such that f x = g x + 6 x f 1 = 4 g 1 - 3 = 9 f 2 = 3 g 2 = 12 Then which of the followin29 Jan, 2023 (E)Differentiability
  49. 49If the function f x = 1 + | cos x | | cos x | , 0 x 2 , x = 2 e cot 6 x cot 4 x , 2 x is continuous at x = 2 , then 9 + 6 log c + 6 - e 6 is25 Jan, 2023 (E)Continuity
  50. 50Let f x = x 2 sin 1 x ; x 0 0 ; x = 0 , then at x = 024 Jan, 2023 (M)Differentiability

Frequently Asked Questions

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

This chapter includes 154 questions compiled from JEE Main papers spanning 2002 to 2026.

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

These are JEE Main questions specifically for the Continuity and Differentiability chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Continuity and Differentiability an important chapter for JEE Main Mathematics?

Continuity and Differentiability has appeared in 23 of the 25 years of JEE Main papers covered here, with 154 questions across 133 papers - about one per paper it appears in.

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

Of the 154 questions analysed for this chapter, 21% are easy, 42% moderate and 37% tough. 2021 had the most, with 28 questions.

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

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

  • Differentiability - 81 questions (53%)
  • Continuity - 73 questions (47%)
  • Differentiability has produced the most tough questions (34).
6.Is Continuity and Differentiability's weightage in JEE Main going up or down?

Across all 133 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 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.