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Mathematics - Limits

Practise 90 NTA Abhyas (JEE Main) questions on Limits. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Limits has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 90 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. 1The value of lim x → 0 ⁡ 1 - cos ⁡ 4 x 5 + cos ⁡ x x tan ⁡ 5 x is equal to
  2. 2The value of lim x → ∞ ( 3 x − 4 3 x + 2 ) x + 1 3 is equal to
  3. 3The value of l i m x → 0 e x - x - 1 x - sin ⁡ x l n 1 + x x 6 is equal to
  4. 4The value of lim x → 0 + ⁡ x cot ⁡ x + x ln ⁡ x is equal to
  5. 5The value of l i m x → 1 - π - 4 t a n - 1 x 1 - x is equal to
  6. 6The value of lim x → 2 π ⁡ 1 - sec ⁡ x sec ⁡ x ln ⁡ sec ⁡ x is equal to
  7. 7The value of lim x e 2 1 + 2 x x x is equal to
  8. 8The value of lim x → 2 ⁡ ∑ r = 1 7 x r - 2 r 2 r x - 2 is equal to
  9. 9The value of lim x 0 - 4 3 x + 15 2 1 x 2 1 + 6 x + 6 2 1 x is equal to
  10. 10The value of l i m x → π 3 2 - 3 sin ⁡ x - cos ⁡ x 3 x - π 2 is equal to the reciprocal of the number
  11. 11The value of lim x → 0 ⁡ 1 - cos 3 ⁡ x sin 2 ⁡ x cos ⁡ x is equal to
  12. 12The value of l i m x → 0 e - x 2 2 - cos ⁡ x x 3 tan ⁡ x is equal to
  13. 13Let lim x → 0 ⁡ sin ⁡ 2 x tan ⁡ x k = L 1 and lim x → 0 ⁡ e 2 x - 1 x = L 2 , and the value of L 1 L 2 is 8, then k is
  14. 14The value of l i m n → ∞ cos ⁡ x c o s x 2 c o s x 4 . . . c o s x 2 n is equal to
  15. 15If f x = tan x 2 , x 0 , 3 , then f 4 (where, . is the greatest integer function)
  16. 16The value of l i m x → 0 t a n 2 3 x 5 - 4 + s e c x is equal to
  17. 17The value of l i m x → - ∞ x 2 t a n 1 x 4 x 2 - x + 1 is equal to
  18. 18If p, q, r, s 0 , then lim x → ∞ p 1 x + q 1 x + r 1 x + s 1 x 4 3 x is equal to
  19. 19If L = l i m x 0 e - x 2 2 - cos x x 2 t a n 2 x , then the value of 3 L is equal to
  20. 20The value of lim x 0 log ( 1 + x + x 2 ) + log ( 1 x + x 2 ) sec x cos x is equal to
  21. 21The value of lim x → π ⁡ tan ⁡ π cos 2 ⁡ x sin 2 ⁡ 2 x is equal to
  22. 22The value of l i m n → ∞ 1 2 - 2 2 + 3 2 - 4 2 + 5 2 . . . . + 2 n + 1 2 n 2 is equal to
  23. 23The value of lim x → 0 ⁡ cos ⁡ x + sin ⁡ b x a x is equal to
  24. 24If l i m x 0 x 1 + a cos x - b sin x x 3 = 1 , then the value of a b is equal to
  25. 25The value of lim x → 0 ⁡ 1 - cos 4 ⁡ x 5 sin 2 ⁡ x cos ⁡ x is equal to
  26. 26The value of l i m x → 1 x t a n x x - 1 is equal to (where x denotes the fractional part of x )
  27. 27The value of l i m x → 1 x 2 5 - 2 x 5 + 1 x - 1 2 is equal to
  28. 28The value of lim x → 0 1 - cos 2 x 3 + cos x x tan 4 x is equal to
  29. 29If l i m x → 0 sin ⁡ 2 x - a sin ⁡ x x 3 exists finitely, then the value of a is
  30. 30If f x = g x 1 x 1 ; x 1 1 ; x = 1 and g 1 = 2 , g 1 = 1 , then lim x 1 f x is equal to
  31. 31The value of lim x → ∞ ⁡ 2 x 1 / 2 + 3 x 1 / 3 + 4 x 1 / 4 + . . . . . + x 1 / n 2 x - 3 1 / 2 + 2 x - 3 1 / 3 + . . . . + 2 x - 3 1 / n is
  32. 32The value of lim x → 0 ⁡ 9 ln ⁡ 2 - cos ⁡ 25 x 5 ln 2 sin ⁡ 3 x + 1 ⁡ is equal to
  33. 33The value of l i m x 0 l n 10 - 9 cos 2 x l n 2 sin 3 x + 1 is equal to
  34. 34The value of l i m n x + 2 2 x + 3 2 x + . . . . . + n 2 x 1 2 + 2 2 + 3 2 + . . . . + n 2 is equal to (where x represents the greatest inte
  35. 35The value of lim x → π 2 ⁡ x 3 ln sin ⁡ x (where, . denotes the greaest integer function)
  36. 36The value of l i m x → 0 sec ⁡ x + tan ⁡ x 1 x is equal to
  37. 37If f x is a polynomial satisfying f x f 1 x = f x + f 1 x and f 2 1 , then lim x → 1 f x is
  38. 38The value of lim x → ∞ ⁡ 3 x - 4 3 x + 2 x + 1 3 is equal to
  39. 39If lim x 0 1 + p x + q x 2 c o s e c x = 2048 , then the value of p 11 is equal to (take ln 2 = 0 .69 )
  40. 40The value of l i m x → 0 - 2 1 x + 2 3 x 3 2 1 x + 5 2 3 x is
  41. 41The value of lim x 1 + 1 x t - 1 dt sin ( x - 1 ) is equal to
  42. 42The value of l i m x → 0 sec ⁡ x - sec ⁡ x s e c x 1 - sec ⁡ x + ln ⁡ sec ⁡ x is equal to
  43. 43The value of lim x → π 4 ⁡ sin ⁡ 2 x sec 2 ⁡ 2 x is equal to
  44. 44The value of lim x → - ∞ ⁡ x 2 tan ⁡ 2 x 16 x 2 - x + 1 is equal to
  45. 45The value of lim x → 0 + ⁡ x x 2 + x x x is equal to
  46. 46If lim x → 0 ⁡ sin - 1 ⁡ x - tan - 1 ⁡ x x 3 equals L , then the value of ( 4 L + 1 ) is
  47. 47The value of lim x → 1 - ⁡ 2 π - 4 sin - 1 ⁡ x 1 - x is equal to
  48. 48The value of l i m x → ∞ ln ⁡ x 2 2 + 3 x 2 is equal to
  49. 49The value of lim x → 0 x 6 0 0 0 - sin x 6 0 0 0 x 2 sin x 6 0 0 0 is
  50. 50The value of lim x 2 1 1 cos 2 x + 2 1 cos 2 x + . + 10 1 cos 2 x cos 2 x is equal to

Frequently Asked Questions

1.How many questions are available for Limits?

This chapter includes 90 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 Limits 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 Limits questions in NTA Abhyas (JEE Main)?

Of the 90 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Limits should I focus on?

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