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Mathematics - Continuity and Differentiability

Practise 93 NTA Abhyas (JEE Main) questions on Continuity and Differentiability. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Continuity and Differentiability has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 93 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1In ( 0 , 2 π ) , the total number of points where f x = m a x . sin ⁡ x , cos ⁡ x , 1 – cos ⁡ x is not differentiable, are equal to
  2. 2Let f x = 1 + cos x x 2 sin 2 x ln 1 + 2 2 x + x 2 x x = is continuous at x = , then is equal to
  3. 3Let f x = min ⁡ 4 - x 2 , 1 + x 2 ∀ x ∈ - 2 , 2 , then the number of points where f x is non-differentiable is
  4. 4If function f x = a x + 7 ; 0 ≤ x 2 b x + 1 ; x ≥ 2 is differentiable ∀ x ≥ 0 , then 2 a + 4 b is equal to
  5. 5If the function f x = a x + 7 : 0 ≤ x 9 b x + 5 : x ≥ 9 is differentiable for x ≥ 0 , then the value of 5 a + 6 b is equal to
  6. 6If f x = e 2 x + 2 x - 1 2 x + 2 x : x 0 1 : x = 0 , then (where, [.] represents the greatest integer function)
  7. 7The number of discontinuity of the greatest integer function f x = x , x ∈ - 7 2 , 100 is equal to
  8. 8The value of f 0 , such that f x = 1 x 2 1 - c o s s i n x can be made continuous at x = 0 , is
  9. 9If f x = a + b c o s x + c s i n x x 2 ; x 0 9 ; x ≤ 0 is continuous at x = 0 , then the value of a + b 5 is
  10. 10The function f x = l i m n x - 2 2 n - 1 x - 2 2 n + 1 n N is discontinuous at
  11. 11If f x = e 1 + 1 x - a e 1 x + 1 : x ≠ 0 b : x = 0 (where a and b are arbitrary constants) is continuous at x = 0 , then the value of a 2 is
  12. 12If f x = a + c o s - 1 x + b : x ≥ 1 - x : x 1 is differentiable at x = 1 , then the value of b - a is equal to
  13. 13If f x = e 2 x + 2 x + 1 - 1 2 x + 2 x + 1 : x ≠ 0 1 : x = 0 , then (where, . represents the greatest integer function)
  14. 14If the function f x = a x + 7 ; 0 ≤ x 2 b x + 5 ; x ≥ 2 is differentiable ∀ x ≥ 0, then 2 a + 4 b is equal to
  15. 15If f x = 5 x + 4 tan ⁡ x x x ≠ 0 k x = 0 , then f x is continuous at x = 0 for
  16. 16If f x = x 2 + x 2 1 + x 2 + x 2 1 + x 2 2 + . … … . . upto ∞, then
  17. 17Let f x = x x 2 + x x 2 + x x 2 + x x 2 , ∀ x ∈ 0,10 (where · and · are the greatest integer and fractional part functions respectively). Th
  18. 18Consider the function f x = min ⁡ x 2 - 4 , x 2 - 1 , then the number of points where f x is non-differentiable is/are
  19. 19If f x = - 2 sin x x 3 2 p cos x + q 3 2 x 2 cos x - 2 2 x 5 2 r sin x 5 2 x 3 is continuous in , 3 , then the number of points at which f x
  20. 20If f x = max ⁡ x n , sin ⁡ π x , n ∈ N has maximum points of non-differentiability for x ∈ ( 0 , 4 ) , then n cannot be
  21. 21Let f : R → R be a function defined as f x = 6 i f x ≤ 1 a + b x i f 1 x 3 b + 5 x i f 3 ≤ x 5 15 i f x ≥ 5 . Then, f is
  22. 22If f x = e x + x - 1 x + x : x ≠ 0 - 1 : x = 0 (where . denotes the greatest integer function), then
  23. 23If f x = 4 + a x − 4 − a x x , − 1 ≤ x 0 3 x + 2 x − 8 , 0 ≤ x ≤ 1 is continuous in [ − 1 , 1 ], then the value of a is
  24. 24Which of the following is a correct statement?
  25. 25Let f x = a ; x = π 2 2 x - π 9 + 2 x - π - b ; x π 2 . If f x is continuous at x = π 2 , then the value of a 2 5 b is
  26. 26Let the function f x = x 2 sin ⁡ 1 x ∀ x ≠ 0 is continuous at x = 0 . Then, the value of the function at x = 0 is
  27. 27If f : R → R is a function defined by f ( x ) = x s i n 2 x - 1 2 π , where x denotes the greatest integer function, then f is
  28. 28Let f x = x 3 x - 1 1 - cos ⁡ x for x ≠ 0 . Then value of f 0 , which make f x continuous at x = 0, is
  29. 29If f x = e 2 x - 1 e 2 x + 1 : x ≠ 0 0 : x = 0 , then f x is
  30. 30Let f , g and h are differentiable functions. If f 0 = 1 ; g 0 = 2 ; h 0 = 3 and the derivatives of their pair wise products at x = 0 are fg
  31. 31Let f : R → R be a function such that f x + y 3 = f x + f y 3 , f 0 = 0 and f ′ 0 = 5 , then
  32. 32If f x = p x + q x 2 x 2 - 5 x + 6 2 x 3 a x 2 + b x + 1 x 3 is differentiable everywhere, then p + q + 1 a + 1 b is equal to
  33. 33Consider the function f x = m a x sin x , cos x , x 0,3 . If is the number of points at which f x is non-differentiable, then the value of 3
  34. 34For a differentiable function f x , if f ' 2 = 2 and f ' 3 = 1 , then the value of lim x 0 f x 2 + x + 2 f 2 f x 2 x + 3 f 3 is equal to
  35. 35If f x = 1 + 5 + x - a x - 4 0 x 4 b x 4 is continuous at x = 4 , then value of 1 a b is equal to
  36. 36If f x = p x + q : x 2 x 2 - 5 x + 6 : 2 x 3 a x 2 + b x + 1 : x 3 is differentiable everywhere, then p + q + 1 a + 1 b is equal to
  37. 37The value of f 0 such that the function f x = 1 + 2 x 3 - 1 + x 4 x is continuous at x = 0 , is
  38. 38Let f x = 10 - x - 5 , x ∈ R , then the set of all values of x at which f f x is not differentiable is
  39. 39On differentiating tan − 1 [ 1 + x 2 − 1 x ] with respect to x , the result would be
  40. 40If the function f x = 1 - x 2 tan ⁡ π x 2 is continuous at x = 1 , then f 1 is equal to
  41. 41Consider the function f x = sin x - 4 . tan - 1 1 x - 4 x 4 0 x = 4 , then
  42. 42Let f x = 1 cos x 2 x 2 tan 2 x ln 1 + 4 2 4 x + x 2 : x 2 : x = 2 is continuous at x = 2 , then the value of is equal to
  43. 43If f x = x x - 1 , then the points of discontinuity of the function f 15 x , where f n = f o f … … . o f ( n times), are
  44. 44Let f x = 1 + sin x l sin x , - 6 x 0 e tan 2 x tan 3 x , 0 x 6 m , x = 0 is continuous at x = 0 . Then, the values of l and m are
  45. 45If f x = e 2 x 2 + x : x 0 a x + b : x 0 is differentiable at x = 0 , then
  46. 46If f x = 1 + s i n x p sin ⁡ x : - π 6 x 0 q : x = 0 e tan ⁡ 3 x . cot ⁡ 5 x : 0 x π 6 is continuous at x = 0 , then the value of 2 p + 10 l
  47. 47If f x = e 2 x 3 + x x 0 a x + b x ≤ 0 is differentiable at x = 0 , then
  48. 48The number of points where f x = x 2 - 3 x - 4 is non-differentiable is
  49. 49Let f x = l i m n → ∞ x 2 + 2 x + 4 + sin ⁡ π x n - 1 x 2 + 2 x + 4 + sin ⁡ π x n + 1 , then
  50. 50If f x = 2 x - 1 2 tan 3 x x s i n 2 x : : 0 x 6 x = 0 is continuous at x = 0 , then the value of 10 3 l n 2 is equal to

Frequently Asked Questions

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

This chapter includes 93 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Continuity and Differentiability questions in NTA Abhyas (JEE Main)?

Of the 93 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

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

All of this chapter's questions come from a single topic: Uncategorized.