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Mathematics - Application of Derivatives

Practise 281 JEE Main previous year questions on Application of Derivatives, 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.

Application of Derivatives has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 281 questions in all. 25% of them were easy, 56% moderate and 20% tough. Most of its questions came from 2021, with 42 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 5 topics are not weighted equally: Maxima Minima (132 questions, 47%), Tangent Normal (63 questions, 22%), and Monotonicity (59 questions, 21%) have been asked the most. Maxima Minima has also led over the last five years, with 51 questions. Maxima Minima has produced the most tough questions (26).

  1. 1Let be a differentiable function such that for all , and . Then the minimum value of the function , is:05 Apr, 2026 (M)Maxima Minima
  2. 2is equal to:04 Apr, 2026 (E)Maxima Minima
  3. 3The number of critical points of the function in the interval is equal to :02 Apr, 2026 (M)Monotonicity
  4. 4Let be a polynomial of degree , and have extrema at and . If , then is equal to:02 Apr, 2026 (E)Maxima Minima
  5. 5Let be a differentiable function satisfying and let . If p and q are respectively the points of local minima and local maxima of g, then the28 Jan, 2026 (E)Maxima Minima
  6. 6Let be the largest interval in which the function , is24 Jan, 2026 (M)Maxima Minima
  7. 7Consider the following three statements for the function defined by : (I) is differentiable at all . (II) is increasing in . (III) is decrea24 Jan, 2026 (E)Monotonicity
  8. 8Let and the minimum value of the function in the interval be . Then is equal to22 Jan, 2026 (M)Maxima Minima
  9. 9Let be a twice differentiable function such that the quadratic equation in m, has two equal roots for every . If , and is the largest interv21 Jan, 2026 (M)Monotonicity
  10. 10Let be a twice differentiable function such that for all and , where is a real number. Let g (0, { }{4} ) g ( { }{4}, { }{2} )$. Then,21 Jan, 2026 (E)Monotonicity
  11. 11Let the function be strictly increasing in and strictly decreasing in . Then is equal to :-08 Apr, 2025 (E)Monotonicity
  12. 12Let and be the critical points of the function . Let and respectively be the absolute minimum and the absolute maximum values of in the inte07 Apr, 2025 (M)Maxima Minima
  13. 13Let be a polynomial function of degree four having extreme values at and . If , then is equal to :07 Apr, 2025 (E)Maxima Minima
  14. 14Let . If the function attains its local maximum and minimum values at the points and respectively such that , then is equal to :-04 Apr, 2025 (E)Maxima Minima
  15. 15Let f be a differentiable function on such that , . Let . Then the number of times the curve meets x -axis is :-04 Apr, 2025 (E)Maxima Minima
  16. 16The shortest distance between the curves and is :03 Apr, 2025 (E)Tangent Normal
  17. 17Let be a function defined by . If is the number of points of local minima and is the number of points of local maxima of , then is03 Apr, 2025 (E)Monotonicity
  18. 18If the function , where , attains its local maximum and local minimum values at and , respectively, such that , then is equal to:02 Apr, 2025 (M)Maxima Minima
  19. 19The sum of all local minimum values of the function is28 Jan, 2025 (M)Maxima Minima
  20. 20Let be the largest open interval in which the function is strictly increasing and (b, c) be the largest open interval, in which the function24 Jan, 2025 (E)Monotonicity
  21. 21If the set of all values of a, for which the equation has three distinct real roots, is the interval , then is equal to ______23 Jan, 2025 (M)Maxima Minima
  22. 22A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm , the 23 Jan, 2025 (E)Rate Measure Error and Approximation
  23. 23A variable line passes through the point and intersects the positive coordinate axes at the points and . The minimum area of the triangle , 09 Apr, 2024 (M)Maxima Minima
  24. 24Let the set of all positive values of , for which the point of local minimum of the function satisfies , be . Then is equal to _________09 Apr, 2024 (M)Maxima Minima
  25. 25Let the set of all values of , for which does not have any critical point, be the interval . Then is equal to _______09 Apr, 2024 (E)Monotonicity
  26. 26For the function , between the following two statements (S1) for only one value of in . (S2) is decreasing in and increasing in .08 Apr, 2024 (M)Monotonicity
  27. 27Let . The number of points of local maxima of in interval is08 Apr, 2024 (M)Maxima Minima
  28. 28The number of critical points of the function is08 Apr, 2024 (M)Monotonicity
  29. 29If the function has a local maximum at and a local minimum at , then and are the roots of the equation :08 Apr, 2024 (E)Maxima Minima
  30. 30Let be the region enclosed by the parabola and the line . Then the maximum area of the rectangle inscribed in the region is________08 Apr, 2024 (E)Maxima Minima
  31. 31The interval in which the function , is strictly increasing is06 Apr, 2024 (M)Maxima Minima
  32. 32If the function attains the maximum value at then :06 Apr, 2024 (E)Maxima Minima
  33. 33Let a rectangle of sides 2 and 4 be inscribed in another rectangle such that the vertices of the rectangle lie on the sides of the rectangle05 Apr, 2024 (M)Maxima Minima
  34. 34For the function consider the following two statements : (I) is increasing in . (II) is decreasing in . Between the above two statements,05 Apr, 2024 (M)Maxima Minima
  35. 35Let the maximum and minimum values of be and , respectively. Then is equal to _________05 Apr, 2024 (E)Maxima Minima
  36. 36Let be a real valued function. If and are respectively the minimum and the maximum values of , then is equal to04 Apr, 2024 (E)Maxima Minima
  37. 37Let be a thrice differentiable function such that and . Then, the minimum number of zeros of is _______04 Apr, 2024 (E)Mean Value Theorem
  38. 38If 5 f x + 4 f 1 x = x 2 − 2 , ∀ x ≠ 0 and y = 9 x 2 f x , then y is strictly increasing in:01 Feb, 2024 (M)Monotonicity
  39. 39Let g : R → R be a non constant twice differentiable such that g ' 1 2 = g ' 3 2 . If a real valued function f is defined as f ( x ) = 1 2 [30 Jan, 2024 (M)Mean Value Theorem
  40. 40Let f x = x + 3 2 x - 2 3 , x ∈ [ - 4 , 4 ] . If M and m are the maximum and minimum values of f , respectively in [ - 4 , 4 ] , then the va30 Jan, 2024 (E)Maxima Minima
  41. 41The function f x = 2 x + 3 x 2 3 , x ∈ R , has29 Jan, 2024 (E)Maxima Minima
  42. 42The function f x = x x 2 - 6 x - 16 , x ∈ ℝ - - 2 , 829 Jan, 2024 (E)Monotonicity
  43. 43Let g ( x ) = 3 f x 3 + f ( 3 - x ) and f " ( x ) 0 for all x ∈ ( 0 , 3 ) . If g is decreasing in ( 0 , α ) and increasing in ( α , 3 ) , th27 Jan, 2024 (E)Monotonicity
  44. 44max 0 x x - 2 sin x cos x + 1 3 sin 3 x =13 Apr, 2023 (M)Maxima Minima
  45. 45The set of all a for which the equation x | x - 1 | + | x + 2 | + a = 0 has exactly one real root, is13 Apr, 2023 (M)Monotonicity
  46. 46If the total maximum value of the function f x = 3 e 2 sin x sin 2 x , x 0 , 2 , is k e , then k e 8 + k 8 e 5 + k 8 is equal to12 Apr, 2023 (M)Maxima Minima
  47. 47Let f : 2 , 4 be a differentiable function such that x log e x f x + log e x f x + f x 1 , x 2 , 4 with f 2 = 1 2 and f 4 = 1 2 . Consider t11 Apr, 2023 (M)Monotonicity
  48. 48A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to fo10 Apr, 2023 (M)Rate Measure Error and Approximation
  49. 49Let g x = f x + f 1 - x and f x 0 , x 0 , 1 . If g is decreasing in the interval 0 , and increasing in the interval , 1 , then tan - 1 2 + t10 Apr, 2023 (E)Monotonicity
  50. 50In the figure, 1 + 2 = 2 and 3 BE = 4 AB . If the area of CAB is 2 3 - 3 unit 2 , when 2 1 is the largest, then the perimeter (in unit) of C10 Apr, 2023 (E)Maxima Minima

Frequently Asked Questions

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

This chapter includes 281 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 Application of Derivatives chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

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

Application of Derivatives has appeared in 25 of the 25 years of JEE Main papers covered here, with 281 questions across 164 papers - about 2 per paper it appears in.

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

Of the 281 questions analysed for this chapter, 25% are easy, 56% moderate and 20% tough. 2021 had the most, with 42 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 - 132 questions (47%)
  • Tangent Normal - 63 questions (22%)
  • Monotonicity - 59 questions (21%)
  • Maxima Minima has produced the most tough questions (26).
6.Is Application of Derivatives's weightage in JEE Main going up or down?

Across all 164 papers analysed, Application of Derivatives has averaged about 1.7 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.