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Mathematics - Limits

Practise 147 JEE Main previous year questions on Limits, 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.

Limits has been asked in 22 of the 25 years of JEE Main papers analysed (2002–2026), with 147 questions in all. 23% of them were easy, 50% moderate and 27% tough. Most of its questions came from 2024, with 22 questions that year. In the last three years (2024–2026) it had 39 questions across 49 papers, about 0.8 per paper.

The chapter's 6 topics are not weighted equally: Trigonometric and Inverse Trigonometric limits (46 questions, 31%), Algebraic and Rational Limits (34 questions, 23%), and Miscellaneous (27 questions, 18%) have been asked the most. Over the last five years the most frequent topics have been Miscellaneous (20), Trigonometric and Inverse Trigonometric limits (15), and Algebraic and Rational Limits (13). Trigonometric and Inverse Trigonometric limits has produced the most tough questions (11).

  1. 1The value of is:06 Apr, 2026 (M)Trigonometric and Inverse Trigonometric limits
  2. 2Let for some . If the set of all possible values of , such that the roots of the equation lie in , be the interval , then equals :06 Apr, 2026 (E)Trigonometric and Inverse Trigonometric limits
  3. 3The product of all possible values of , for which , is:05 Apr, 2026 (M)Trigonometric and Inverse Trigonometric limits
  4. 4Let . Then the number of solutions of the equation , is :05 Apr, 2026 (E)Trigonometric and Inverse Trigonometric limits
  5. 5If , then is equal to :02 Apr, 2026 (M)Existance of Limit
  6. 6The value of is equal to28 Jan, 2026 (M)Exponential and logarithmic limits
  7. 7If , then is equal to :22 Jan, 2026 (E)Miscellaneous
  8. 8Let be a twice differentiable function such that and . Then is equal to :21 Jan, 2026 (M)Exponential and logarithmic limits
  9. 9Let denote the greatest integer function and . Then is equal to .21 Jan, 2026 (E)Miscellaneous
  10. 10Given below are two statements : Statement I : Statement II : In the light of the above statements, choose the correct answer from the optio08 Apr, 2025 (E)Exponential and logarithmic limits
  11. 11is equal to07 Apr, 2025 (M)Existance of Limit
  12. 12If the function is continuous at , then is equal to ________07 Apr, 2025 (E)Trigonometric and Inverse Trigonometric limits
  13. 13If , where , then is equal to04 Apr, 2025 (M)Miscellaneous
  14. 14If , then is equal to ______03 Apr, 2025 (E)Special Forms
  15. 15For , if , then is equal to:02 Apr, 2025 (M)Algebraic and Rational Limits
  16. 16If is finite, then is equal to :02 Apr, 2025 (E)Miscellaneous
  17. 17Let [t] be the greatest integer less than or equal to t. Then the least value of \( {p} {N}\) for which \( _{x 0^{+}} (x ( [ {1}{x} ]+ [ {2}29 Jan, 2025 (M)Miscellaneous
  18. 18If , then is equal to ________29 Jan, 2025 (E)Special Forms
  19. 19Let . Then is equal to28 Jan, 2025 (E)Exponential and logarithmic limits
  20. 20is:24 Jan, 2025 (M)Algebraic and Rational Limits
  21. 21is equal to :23 Jan, 2025 (E)Exponential and logarithmic limits
  22. 22If , then the value of equals :22 Jan, 2025 (E)Algebraic and Rational Limits
  23. 23Let be , using only the principal values of the inverse trigonometric functions. Then is equal to ________09 Apr, 2024 (M)Miscellaneous
  24. 24is equal to09 Apr, 2024 (E)Algebraic and Rational Limits
  25. 25is equal to09 Apr, 2024 (E)Exponential and logarithmic limits
  26. 26The value of is08 Apr, 2024 (M)Trigonometric and Inverse Trigonometric limits
  27. 27If and are the roots of the quadratic equation , then is equal to__________08 Apr, 2024 (E)Special Forms
  28. 28Let be a differentiable function such that . Then is equal to06 Apr, 2024 (M)Miscellaneous
  29. 29is equal to :06 Apr, 2024 (E)Miscellaneous
  30. 30Let be a differentiable function in the interval such that and for each . Then is equal to _______05 Apr, 2024 (M)Algebraic and Rational Limits
  31. 31Let be a root of the equation . If , where , then is equal to_______05 Apr, 2024 (E)Algebraic and Rational Limits
  32. 32If , where , then is equal to______04 Apr, 2024 (M)Algebraic and Rational Limits
  33. 33Let . Then, is equal to04 Apr, 2024 (E)Miscellaneous
  34. 34Let x denote the fractional part of x and f x = cos − 1 1 − x 2 sin − 1 1 − x x − x 3 , x ≠ 0 . If L and R respectively denotes the left han01 Feb, 2024 (M)Existance of Limit
  35. 35Let f x = x − 1 , x is even , 2 x , x is odd , x ∈ N . If for some a ∈ N , f f f a = 21 , then lim x → a − x 3 a − x a , where t denotes the01 Feb, 2024 (E)Existance of Limit
  36. 36lim x → 0 e 2 sin x - 2 sin x - 1 x 231 Jan, 2024 (M)Miscellaneous
  37. 37Let a be the sum of all coefficients in the expansion of ( 1 – 2 x + 2 x 2 ) 2023 ( 3 - 4 x 2 + 2 x 3 ) 2024 and b = lim x → 0 ∫ 0 x log 1 +31 Jan, 2024 (M)Miscellaneous
  38. 38Let f : → R → 0 , ∞ be strictly increasing function such that lim x → ∞ f 7 x f x = 1 . Then, the value of lim x → ∞ f 5 x f x − 1 is equal 31 Jan, 2024 (E)Algebraic and Rational Limits
  39. 39If lim x → 0 a x 2 e x − b log e 1 + x + c x e − x x 2 sin x = 1 , then 16 a 2 + b 2 + c 2 is equal to ______.31 Jan, 2024 (E)Miscellaneous
  40. 40Let f : - π 2 , π 2 → R be a differentiable function such that f 0 = 1 2 , If lim x → 0 x ∫ 0 x f ( t ) d t e x 2 - 1 = α , then 8 α 2 is eq30 Jan, 2024 (M)Miscellaneous
  41. 41lim x → π 2 1 x - π 2 2 ∫ x 3 π 2 3 cos 1 t 3 d t is equal to29 Jan, 2024 (M)Miscellaneous
  42. 42Let the slope of the line 45 x + 5 y + 3 = 0 be 27 r 1 + 9 r 2 2 for some r 1 , r 2 ∈ R . Then lim x → 3 ∫ 3 x 8 t 2 3 r 2 x 2 - r 2 x 2 - r29 Jan, 2024 (E)Miscellaneous
  43. 43If a = lim x → 0 1 + 1 + x 4 - 2 x 4 and b = lim x → 0 sin 2 x 2 - 1 + cos x , then the value of a b 3 is :27 Jan, 2024 (M)Algebraic and Rational Limits
  44. 44If lim x → 0 3 + α sin x + β cos x + log e ( 1 - x ) 3 tan 2 x = 1 3 , then 2 α - β is equal to :27 Jan, 2024 (E)Miscellaneous
  45. 45If lim x 0 e a x - cos ( b x ) - c x e - c x 2 1 - cos ( 2 x ) = 17 , then 5 a 2 + b 2 is equal to13 Apr, 2023 (E)Miscellaneous
  46. 46lim x 0 1 - cos 2 ( 3 x ) cos 3 ( 4 x ) sin 3 ( 4 x ) log e 2 x + 1 5 is equal to08 Apr, 2023 (M)Trigonometric and Inverse Trigonometric limits
  47. 47If 0 are the roots of the equation a x 2 + b x + 1 = 0 , and lim x 1 1 - cos x 2 + b x + a 2 ( 1 - x ) 2 1 2 = 1 k 1 - 1 , then k is equal t08 Apr, 2023 (E)Trigonometric and Inverse Trigonometric limits
  48. 48lim n 2 1 2 - 2 1 3 2 1 2 - 2 1 5 . . . . 2 1 2 - 2 1 2 n + 1 is equal to06 Apr, 2023 (E)Miscellaneous
  49. 49lim x 3 x + 1 + 3 x - 1 6 + 3 x + 1 - 3 x - 1 6 x + x 2 - 1 6 + x - x 2 - 1 6 x 331 Jan, 2023 (E)Miscellaneous
  50. 50Let f , g and h be the real valued functions defined on as f x = x x , x 0 1 , x = 0 , g x = sin x + 1 x + 1 , x - 1 1 , x = - 1 and h x = 230 Jan, 2023 (E)Trigonometric and Inverse Trigonometric limits

Frequently Asked Questions

1.How many questions are available for Limits?

This chapter includes 147 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 Limits chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Limits an important chapter for JEE Main Mathematics?

Limits has appeared in 22 of the 25 years of JEE Main papers covered here, with 147 questions across 129 papers - about one per paper it appears in.

4.What is the difficulty level of Limits questions in JEE Main?

Of the 147 questions analysed for this chapter, 23% are easy, 50% moderate and 27% tough. 2024 had the most, with 22 questions.

5.Which topics in Limits should I focus on?

These topics have carried the most weightage in Limits:

  • Trigonometric and Inverse Trigonometric limits - 46 questions (31%)
  • Algebraic and Rational Limits - 34 questions (23%)
  • Miscellaneous - 27 questions (18%)
  • Trigonometric and Inverse Trigonometric limits has produced the most tough questions (11).
6.Is Limits's weightage in JEE Main going up or down?

Across all 129 papers analysed, Limits has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.