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Mathematics - Application of Derivatives

Practise 68 JEE Advanced previous year questions on Application of Derivatives, compiled from papers spanning 2006 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 Advanced tests.

Application of Derivatives has been asked in 20 of the 27 years of JEE Advanced papers analysed (2000–2026), with 68 questions in all. 15% of them were easy, 40% moderate and 46% tough. Most of its questions came from 2017, with 6 questions that year. In the last three years (2024–2026) it had 6 questions across 6 papers, about 1 per paper.

The chapter's 4 topics are not weighted equally: Maxima Minima (32 questions, 47%), Monotonicity (21 questions, 31%), and Mean Value Theorem (10 questions, 15%) have been asked the most. Over the last five years the most frequent topics have been Monotonicity (4), Maxima Minima (2), and Tangent Normal (1). Maxima Minima has produced the most tough questions (12).

  1. 1Consider the function given by . Then which one of the following statements is TRUE?2026 (Paper 1)Maxima Minima
  2. 2Let be the point on the parabola such that the slope of the tangent to the parabola at the point is . Let be the point in the first quadrant2026 (Paper 1)Tangent Normal
  3. 3Let denote the set of all real numbers. Define the function by Then which one of the following statements is TRUE ?2025 (Paper 1)Monotonicity
  4. 4Let denote the set of all real numbers. For a real number , let denote the greatest integer less than or equal to . Let denote a natural num2025 (Paper 1)Maxima Minima
  5. 5Let denote the set of all real numbers. Let be defined by Then which of the following statements is (are) TRUE?2025 (Paper 2)Monotonicity
  6. 6Let the function be defined by . Then the number of solutions of in is2024 (Paper 2)Monotonicity
  7. 7Let S be the set of all twice differentiable functions f from to such that d 2 f d x 2 x 0 for all x - 1 , 1 . For f S , let X f be the numb2023 (Paper 2)Monotonicity
  8. 8Let f : R R be defined by f x = x 2 - 3 x - 6 x 2 + 2 x + 4 Then which of the following statements is(are) TRUE?2021 (Paper 1)Maxima Minima
  9. 9Let and be defined by and where, for any positive integer and real numbers denotes the product of Let and , respectively, denote the number 2021 (Paper 2)Maxima Minima
  10. 10Let and be defined by f_{2}(x)=98(x-1)^{50}-600(x-1)^{49}+2450, x > 0 n a_{1}, a_{2}, , a_{n}, _{i=1}^{n} a_{i} a_{1}, a_{2}, , a_{n} . m_{i2021 (Paper 2)Maxima Minima
  11. 11Paragraph: Let and be functions such that , , , and Question: Which of the following statements is TRUE ?2021 (Paper 2)Monotonicity
  12. 12Paragraph: Let and be functions such that , , , and Question: Which of the following statements is TRUE ?2021 (Paper 2)Monotonicity
  13. 13Let a , b and be positive real numbers. Suppose P is an end point of the latus rectum of the parabola y 2 = 4 x , and suppose the ellipse x 2020 (Paper 1)Tangent Normal
  14. 14Consider all rectangles lying in the region x , y R R : 0 x 2 a n d 0 y 2 sin 2 x and having one side on the x -axis. The area of the rectan2020 (Paper 1)Maxima Minima
  15. 15For a polynomial g x with real coefficients, let m g denote the number of distinct real roots of g x . Suppose S is the set of polynomials w2020 (Paper 1)Mean Value Theorem
  16. 16Let the function f : 0 , be defined by f = sin + cos 2 + sin - cos 4 . Suppose the function f has a local minimum at precisely when 1 , , r 2020 (Paper 2)Maxima Minima
  17. 17Let f : R R be given by f x = x 5 + 5 x 4 + 10 x 3 + 10 x 2 + 3 x + 1 , x 0 ; x 2 - x + 1 , 0 x 1 ; 2 3 x 3 - 4 x 2 + 7 x - 8 3 , 1 x 3 ; x 2019 (Paper 1)Maxima Minima
  18. 18Let f x = sin x x 2 , x 0 . Let x 1 x 2 x 3 x n be all the points of local maximum of f and y 1 y 2 y 3 y n be all the points of local minim2019 (Paper 2)Maxima Minima
  19. 19Let f : R R be given by f x = x - 1 x - 2 x - 5 . Define F x = 0 x f t d t , x 0 . Then which of the following options is/are correct?2019 (Paper 2)Maxima Minima
  20. 20For every twice differentiable function f : R - 2 , 2 w i t h f 0 2 + f 0 2 = 85 , which of the following statement(s) is (are) TRUE?2018 (Paper 1)Mean Value Theorem
  21. 21The number of real solutions of the equation sin - 1 i = 1 x i + 1 - x i = 1 x 2 i = 2 - cos - 1 i = 1 - x 2 i - i = 1 - x i lying in the in2018 (Paper 1)Monotonicity
  22. 22Let f : R 0 , 1 , be a continuous function then, which of the following function(s), has(have) the values zero at some point in the interval2017 (Paper 1)Monotonicity
  23. 23Let f x = x + log e x - x log e x , x 0 , Column 1 contains information about zeros of f ( x ) , f ( x ) and f ( x ) Column 2 contains infor2017 (Paper 1)Monotonicity
  24. 24Let f x = x + log e x - x log e x , x 0 , . Column 1 contains information about zeros of f x , f x and f x . Column 2 contains information a2017 (Paper 1)Monotonicity
  25. 25Let f x = x + log e x - x log e x , x 0 , . Column 1 contains information about zeros of f x , f x and f x . Column 2 contains information a2017 (Paper 1)Monotonicity
  26. 26If f : R R is a twice differentiable function such that f x 0 for all x R and f 1 2 = 1 2 , f 1 = 1 then2017 (Paper 2)Mean Value Theorem
  27. 27If f x = cos 2 x cos 2 x sin 2 x - cos x cos x - sin x sin x sin x cos x , then2017 (Paper 2)Maxima Minima
  28. 28The least value of R for which, 4 x 2 + 1 x 1 , for all x 0 , is2016 (Paper 1)Maxima Minima
  29. 29The total number of distinct x 0 , 1 for which, 0 x t 2 1 + t 4 d t = 2 x - 1 is2016 (Paper 1)Monotonicity
  30. 30A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of V m m 3 , h2015 (Paper 1)Maxima Minima
  31. 31Let f , g : - 1 , 2 R be continuous functions which are twice differentiable on the interval - 1 , 2 . Let the values of f and g at the poin2015 (Paper 2)Monotonicity
  32. 32Paragraph: Let be a thrice differentiable function. Suppose that and $F^{ }(x) Question: The correct statement(s) is(are)2015 (Paper 2)Monotonicity
  33. 33Let f : 0 , R be given by f x = 1 x x e - t + 1 t d t t , then2014 (Paper 1)Monotonicity
  34. 34Let a R and let f : R R be given by f x = x 5 - 5 x + a , then2014 (Paper 1)Mean Value Theorem
  35. 35For every pair of continuous functions f , g : 0 , 1 R such that max f x : x 0 , 1 = max { g x : x 0 , 1 } , then the correct statement (s) 2014 (Paper 1)Mean Value Theorem
  36. 36The slope of the tangent to the curve y - x 5 2 = x 1 + x 2 2 at the point (1, 3) is ________.2014 (Paper 1)Tangent Normal
  37. 37The number of points in - , , for which x 2 - x sin x - cos x = 0 , is:2013 (Paper 1)Mean Value Theorem
  38. 38A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by fold2013 (Paper 1)Maxima Minima
  39. 39The function f x = 2 x + x + 2 - x + 2 - 2 x has a local minimum or a local maximum at x =2013 (Paper 2)Maxima Minima
  40. 40Paragraph: Let (the set of all real numbers) be a function. Suppose the function is twice differentiable, and satisfies Question: Which of t2013 (Paper 2)Mean Value Theorem
  41. 41Paragraph: Let (the set of all real numbers) be a function. Suppose the function is twice differentiable, and satisfies Question: If the fun2013 (Paper 2)Mean Value Theorem
  42. 42A line L : y = m x + 3 meets y - a x is at E(0,3) and the arc of the parabola y 2 = 1 6 x , 0 y 6 at the point F x 0 y 0 .The tangent to the2013 (Paper 2)Maxima Minima
  43. 43Let be defined as . The total number of points at which attains either a local maximum or a local minimum is2012 (Paper 1)Maxima Minima
  44. 44Let be a real polynomial of least degree which has a local maximum at and a local minimum at . If and , then is2012 (Paper 1)Maxima Minima
  45. 45Let for all and let for all . Question: Which of the following is true?2012 (Paper 2)Maxima Minima
  46. 46If for all , then2012 (Paper 2)Maxima Minima
  47. 47The number of distinct real roots of is2011 (Paper 2)Monotonicity
  48. 48Let and be real-valued functions defined on the interval by and . If and denote respectively, the absolute maximum of and on , then2010 (Paper 1)Maxima Minima
  49. 49The maximum value of the expression is2010 (Paper 1)Maxima Minima
  50. 50Let be a function defined on (the set of all real numbers) such that , for all . If is a function defined on with values in the interval suc2010 (Paper 2)Maxima Minima

Frequently Asked Questions

1.How many questions are available for Application of Derivatives?

This chapter includes 68 questions compiled from JEE Advanced papers spanning 2006 to 2026.

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

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

3.Is Application of Derivatives an important chapter for JEE Advanced Mathematics?

Application of Derivatives has appeared in 20 of the 21 years of JEE Advanced papers covered here, with 68 questions across 31 papers - about 2 per paper it appears in.

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

Of the 68 questions analysed for this chapter, 15% are easy, 40% moderate and 46% tough. 2017 had the most, with 6 questions.

5.Which topics in Application of Derivatives should I focus on?

These topics have carried the most weightage in Application of Derivatives:

  • Maxima Minima - 32 questions (47%)
  • Monotonicity - 21 questions (31%)
  • Mean Value Theorem - 10 questions (15%)
  • Maxima Minima has produced the most tough questions (12).
6.Is Application of Derivatives's weightage in JEE Advanced going up or down?

Across all 31 papers analysed, Application of Derivatives has averaged about 2.2 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.