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Mathematics - Limits

Practise 31 JEE Advanced previous year questions on Limits, compiled from papers spanning 2006 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 JEE Advanced tests.

Limits has been asked in 18 of the 27 years of JEE Advanced papers analysed (2000–2026), with 31 questions in all. 16% of them were easy, 65% moderate and 19% tough. Most of its questions came from 2024, with 4 questions that year. In the last three years (2024–2026) it had 6 questions across 6 papers, about 1 per paper.

The chapter's 6 topics are not weighted equally: Algebraic and Rational Limits (12 questions, 39%), Miscellaneous (8 questions, 26%), and Exponential and logarithmic limits (4 questions, 13%) have been asked the most. Algebraic and Rational Limits has also led over the last five years, with 5 questions. Algebraic and Rational Limits has produced the most tough questions (3).

  1. 1Let and be the real numbers such that . Then the value of is _______2025 (Paper 1)Algebraic and Rational Limits
  2. 2Let be the real number such that . For a given real number , define for all real numbers . Then which one of the following statements is TRU2025 (Paper 2)Algebraic and Rational Limits
  3. 3Let be a continuously differentiable function on the interval such that and for each . Then, for all is equal to2024 (Paper 1)Algebraic and Rational Limits
  4. 4Let . If , then the value of is2024 (Paper 2)Trigonometric and Inverse Trigonometric limits
  5. 5Let be the set of all such that . Then which of the following is (are) correct?2024 (Paper 2)Trigonometric and Inverse Trigonometric limits
  6. 6Let the function be defined by Define . Let denote the number of solutions of the equation in the interval and . Then the value of is equal 2024 (Paper 2)Algebraic and Rational Limits
  7. 7Let f : 0 , 1 be the function defined as f x = n if x [ 1 n + 1 , 1 n ) where n . Let g : 0 , 1 be a function such that x 2 x 1 - t t d t g 2023 (Paper 1)Algebraic and Rational Limits
  8. 8Let be a positive real number. Let f : and g : , be the functions defined by f x = sin x 12 and g x = 2 log e x - log e e x - e . Then the v2022 (Paper 1)Exponential and logarithmic limits
  9. 9If = lim x 0 e x 3 - 1 - x 3 1 3 + 1 - x 2 1 2 - 1 sin x x sin 2 x , then the value of 6 is2022 (Paper 2)Exponential and logarithmic limits
  10. 10Let e denote the base of the natural logarithm. The value of the real number a for which the right-hand limit lim x 0 + 1 x 1 e 1 x a is equ2020 (Paper 1)Miscellaneous
  11. 11The value of the limit lim x 2 4 2 sin 3 x + sin x 2 sin 2 x sin 3 x 2 + cos 5 x 2 - 2 + 2 cos 2 x + cos 3 x 2 is _________2020 (Paper 2)Trigonometric and Inverse Trigonometric limits
  12. 12Let F : R R be a function. We say that f has: PROPERTY 1 if lim h 0 f h - f 0 h exists and is finite, and PROPERTY 2 if lim h 0 f h - f 0 h 2019 (Paper 2)Existance of Limit
  13. 13For a R , a 1 , let lim n 1 + 2 3 + + n 3 n 7 / 3 1 a n + 1 2 + 1 a n + 2 2 + + 1 a n + n 2 = 54 . Then the possible value(s) of a is/are:2019 (Paper 2)Miscellaneous
  14. 14For each positive integer n , let y n = 1 n ( ( n + 1 ) ( n + 2 ) ... ( n + n ) ) 1 n . If lim n y n = L , then the value of L (where x is t2018 (Paper 1)Miscellaneous
  15. 15Let f x = 1 - x ( 1 + 1 - x ) | 1 - x | cos 1 1 - x for x 1 , then2017 (Paper 2)Existance of Limit
  16. 16Let , R be such that lim x 0 x 2 sin x x - sin x = 1 . Then 6 + equals2016 (Paper 1)Trigonometric and Inverse Trigonometric limits
  17. 17Let f x = lim n n n x + n x + n 2 . . x + n n n ! x 2 + n 2 x 2 + n 2 4 . . x 2 + n 2 n 2 x n , for all x 0 . Then2016 (Paper 2)Miscellaneous
  18. 18Let f : R 0 , and g : R R be twice differentiable functions such that f and g are continuous functions on R . Suppose f ( 2 ) = g ( 2 ) = 0 2016 (Paper 2)Algebraic and Rational Limits
  19. 19Let f : R R be a continuous odd function, which vanishes exactly at one point and f 1 = 1 2 . Suppose that F x = - 1 x f ( t ) d t for all x2015 (Paper 2)Miscellaneous
  20. 20Let m and n be two positive integers greater than 1. If lim 0 e c o s ( n ) - e m = - e 2 then the value of m n is2015 (Paper 2)Algebraic and Rational Limits
  21. 21The largest value of the non - negative integer a for which lim x 1 - a x + sin x - 1 + a x + sin x - 1 - 1 1 - x 1 - x = 1 4 is _________2014 (Paper 1)Exponential and logarithmic limits
  22. 22If , then2012 (Paper 1)Algebraic and Rational Limits
  23. 23Let and be the roots of the equation where . Then and are2012 (Paper 2)Algebraic and Rational Limits
  24. 24If and , then the value of is2011 (Paper 2)Special Forms
  25. 25The value of is2010 (Paper 1)Algebraic and Rational Limits
  26. 26Let , . If is finite, then2009 (Paper 1)Miscellaneous
  27. 27Let and let be the left hand derivative of at . If , then2008 (Paper 1)Algebraic and Rational Limits
  28. 28Let be differentiable on the interval such that , and for each . Then, is2007 (Paper 1)Miscellaneous
  29. 29equals2007 (Paper 1)Algebraic and Rational Limits
  30. 30For is2006Exponential and logarithmic limits
  31. 31Paragraph: Read the following passage and answer the questions. For every function which is twice differentiable, these will be good approxi2006Miscellaneous

Frequently Asked Questions

1.How many questions are available for Limits?

This chapter includes 31 questions compiled from JEE Advanced papers spanning 2006 to 2025.

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

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

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

Limits has appeared in 18 of the 21 years of JEE Advanced papers covered here, with 31 questions across 24 papers - about one per paper it appears in.

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

Of the 31 questions analysed for this chapter, 16% are easy, 65% moderate and 19% tough. 2024 had the most, with 4 questions.

5.Which topics in Limits should I focus on?

These topics have carried the most weightage in Limits:

  • Algebraic and Rational Limits - 12 questions (39%)
  • Miscellaneous - 8 questions (26%)
  • Exponential and logarithmic limits - 4 questions (13%)
  • Algebraic and Rational Limits has produced the most tough questions (3).
6.Is Limits's weightage in JEE Advanced going up or down?

Across all 24 papers analysed, Limits has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 1.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.