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Mathematics - Continuity and Differentiability

Practise 73 TS EAMCET previous year questions on Continuity and Differentiability, compiled from papers spanning 2001 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty TS EAMCET tests.

Continuity and Differentiability has been asked in 18 of the 24 years of TS EAMCET papers analysed (2001–2024), with 73 questions in all. 49% of them were easy, 40% moderate and 11% tough. Most of its questions came from 2021, with 16 questions that year. In the last three years (2022–2024) it had 9 questions across 17 papers, about 0.5 per paper.

The chapter's 3 topics are not weighted equally: Continuity (51 questions, 70%), Differentiability (21 questions, 29%), and Continuity and Differentiability (1 question, 1%) have been asked the most. Continuity has also led over the last five years, with 18 questions. Continuity has produced the most tough questions (8).

  1. 1If is the greatest integer function and is a real valued function, then is04 May, 2025 (M)Continuity
  2. 2Let be defined by where denotes greatest integer function, then the number of points of discontinuity for the function in is04 May, 2025 (E)Continuity
  3. 3If , then at is04 May, 2025 (E)Continuity and Differentiability
  4. 4The set of all values of for which is differentiable is04 May, 2025 (E)Differentiability
  5. 5The values of at which the real valued function is not differentiable is03 May, 2025 (M)Differentiability
  6. 6If the real valued function is continuous at then03 May, 2025 (E)Continuity
  7. 7If the function is differentiable, then02 May, 2025 (E)Continuity
  8. 8If the real valued function is continuous at , then11 May, 2024 (M)Continuity
  9. 9A function is such that . If , then11 May, 2024 (M)Differentiability
  10. 10If the function is continuous in its domain, then10 May, 2024 (M)Continuity
  11. 11The real valued function is10 May, 2024 (E)Continuity
  12. 12If the function is differentiable at , then10 May, 2024 (E)Differentiability
  13. 13If the function is continuous at , then09 May, 2024 (M)Continuity
  14. 14If is a real valued function, then at is09 May, 2024 (M)Continuity
  15. 15Define by Then the value of ' ' so that is continuous at is09 May, 2024 (E)Continuity
  16. 16Let f x = 3 - x if x - 3 6 if - 3 x 3 3 + x if x 3 . Let be the number of points of discontinuity of f and be the number of points where f i18 Jul, 2022 (E)Continuity
  17. 17If the function defined by , then is equal to06 Aug, 2021 (M)Continuity
  18. 18If is defined as , then is06 Aug, 2021 (M)Differentiability
  19. 19Let and be two differentiable functions satisfying and . Then is equal to06 Aug, 2021 (M)Differentiability
  20. 20is defined as Which of the following is true?06 Aug, 2021 (M)Continuity
  21. 21If defined as (when ) is continuous at , then is equal to06 Aug, 2021 (E)Continuity
  22. 22Match the items given in List A with those of the items of List B The correct match is06 Aug, 2021 (E)Continuity
  23. 23Suppose defined as , where and denote the greatest integer function and the fractional part of respectively, then at06 Aug, 2021 (E)Differentiability
  24. 24If f x = tan ( 2 p - 7 ) x + tan 3 x x , x 0 p - q , x = 0 q x 2 + x - x x 3 2 , x 0 . If f x is continuous at x = 0 , then q p =05 Aug, 2021 (M)Continuity
  25. 25Let f x be differentiable function for all x R and f ( x + y ) = f ( x ) + f ( y ) - 3 x y . If lim h 0 f h h = 7 , then f ' x =05 Aug, 2021 (M)Differentiability
  26. 26The Rolle s theorem is not applicable to f x = x , 0 x 1 2 - x , 1 x 2 on [ 0 , 2 ] because05 Aug, 2021 (M)Differentiability
  27. 27Let a , b , c be three real numbers. If the function f x = cos 2 x + if x 0 a x 2 + b if 0 x 1 c x + 4 if 1 x 2 3 a + 1 if x 2 is continuous05 Aug, 2021 (E)Continuity
  28. 28If f : R R is a differentiable function at a R such that f ' a = a f a , then lim x a x f a - a f x x - a =05 Aug, 2021 (E)Differentiability
  29. 29If f x = 1 + cos x , x 0 a - x , 0 x 2 x 2 - b 2 , x 2 is continuous everywhere, then a 2 + b 2 =04 Aug, 2021 (M)Continuity
  30. 30Let g : - 2 , 2 and f : - 2 , 2 are two functions defined as g x = - 1 , if - 2 x 0 x 2 - 1 , if 0 x 2 and f ( x ) = | g ( x ) | + g ( | x |04 Aug, 2021 (M)Differentiability
  31. 31Consider the following statements. a) If a function is differentiable at a point ' p ' then it is not continuous at ' p ' b) If a function i04 Aug, 2021 (M)Differentiability
  32. 32If the function f x = x x + 3 e - x 2 satisfies all the conditions of the Rolle s theorem in - 3 , 0 , then a root of f ' ( x ) = 0 is04 Aug, 2021 (M)Differentiability
  33. 33If and , then14 Sep, 2020 (M)Differentiability
  34. 34Let be functions defined by and Consider the following statements (i) is continuous at but not differentiable at (ii) is differentiable at ,14 Sep, 2020 (M)Differentiability
  35. 35Define . If is discontinuous at and in and , then14 Sep, 2020 (E)Continuity
  36. 36Assertion (A) , is continuous on Reason (R) is continuous at . The correct option among the following is11 Sep, 2020 (M)Continuity
  37. 37Consider the following statements Statement I If , where are real numbers, then the polynomial has a zero in the interval . Statement II If 11 Sep, 2020 (M)Differentiability
  38. 38A function with has no maximum and has only one minimum at with . Which one of the following is true?11 Sep, 2020 (M)Continuity
  39. 39At is11 Sep, 2020 (E)Continuity
  40. 40If is continuous on , then10 Sep, 2020 (M)Continuity
  41. 41The value of ' ' for which the function , is10 Sep, 2020 (E)Continuity
  42. 42Let x denotes the greatest integer less than or equal to x . Then f x = 1 + sin cos x cos sin x is09 Sep, 2020 (M)Continuity
  43. 43If , then at is09 Sep, 2020 (E)Continuity
  44. 44Let and be real-valued functions. If and , then06 May, 2019 (M)Continuity
  45. 45If the function defined by Is continuous at , then04 May, 2019 (M)Continuity
  46. 46The set of values of for which the function is continuous, is04 May, 2019 (E)Continuity
  47. 47If the function , defined by , then ' ' is04 May, 2019 (E)Continuity
  48. 48If ' ' is the point of discontinuity of the function Then,03 May, 2019 (M)Continuity
  49. 49If the function defined by f x = x 2 + e 1 2 - x - 1 , for x 2 k , for x = 2 is right continuous at x = 2 , then k =03 May, 2019 (E)Continuity
  50. 50If f x = a x + b , if x 1 a x 2 + c , if 1 x 2 d x 2 + 1 x , if x 2 is differentiable on R , then a d - b c =03 May, 2019 (E)Differentiability

Frequently Asked Questions

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

This chapter includes 73 questions compiled from TS EAMCET papers spanning 2001 to 2025.

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

These are TS EAMCET 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 TS EAMCET Mathematics?

Continuity and Differentiability has appeared in 19 of the 25 years of TS EAMCET papers covered here, with 73 questions across 46 papers - about 2 per paper it appears in.

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

Of the 73 questions analysed for this chapter, 49% are easy, 40% moderate and 11% tough. 2021 had the most, with 16 questions.

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

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

  • Continuity - 51 questions (70%)
  • Differentiability - 21 questions (29%)
  • Continuity and Differentiability - 1 question (1%)
  • Continuity has produced the most tough questions (8).
6.Is Continuity and Differentiability's weightage in TS EAMCET going up or down?

Across all 46 papers analysed, Continuity and Differentiability has averaged about 1.6 questions per paper. In the last three years (2022–2024), 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.