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Mathematics - Application of Derivatives

Practise 140 NDA previous year questions on Application of Derivatives, compiled from papers spanning 2010 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 NDA tests.

Application of Derivatives has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 140 questions in all. 16% of them were easy, 80% moderate and 4% tough. Most of its questions came from 2014, with 13 questions that year. In the last three years (2024–2026) it had 20 questions across 5 papers, about 4 per paper.

The chapter's 5 topics are not weighted equally: Maxima Minima (68 questions, 49%), Monotonicity (44 questions, 31%), and Tangent Normal (15 questions, 11%) have been asked the most. Maxima Minima has also led over the last five years, with 21 questions. Maxima Minima has produced the most tough questions (3).

  1. 1What is the length of the longest interval in which the function is decreasing ?2026 (Phase 1)Monotonicity
  2. 2Passage: Let and be the sets where decreases and increases respectively. Question: What is equal to ?2026 (Phase 1)Monotonicity
  3. 3Passage: Let and be the sets where decreases and increases respectively. Question: What is equal to ?2026 (Phase 1)Monotonicity
  4. 4Consider the following for the two (02) items that follow: Let be a triangle right-angled at and units. What is equal to if the area of the 2025 (Phase 1)Maxima Minima
  5. 5Consider the following for the two (02) items that follow: Let be a triangle right-angled at and units. What is the maximum area of the tria2025 (Phase 1)Maxima Minima
  6. 6Consider the following for the two (02) items that follow: The slope of the tangent to the curve at is 4 for every real number and the curve2025 (Phase 1)Rate Measure Error and Approximation
  7. 7Consider the following for the two (02) items that follow: Let the function . Consider the following statements: I. is an increasing functio2025 (Phase 1)Monotonicity
  8. 8For the following three (03) items: Consider the function . Consider the following statements: I. The function is increasing in the interval2025 (Phase 2)Monotonicity
  9. 9For the following three (03) items: Let . What is the slope of the tangent to the curve at ?2025 (Phase 2)Tangent Normal
  10. 10For the following two (02) items: Consider the function . The function has2025 (Phase 2)Maxima Minima
  11. 11A wire of length 20 cm is to be bent into a rectangle. Which of the following statements is/are correct? I. The rectangle of the largest are2025 (Phase 2)Maxima Minima
  12. 12Consider the following statements regarding the function : Statement-I: is decreasing on the intervals . Statement-II: for all . Which one o2025 (Phase 2)Monotonicity
  13. 13Consider the following statements: Statement-I: The function has a minimum value 48 at . Statement-II: As increases through 4, changes sign 2025 (Phase 2)Maxima Minima
  14. 14The non-negative values of for which the function has neither maximum nor minimum in the range is:2024 (Phase 1)Maxima Minima
  15. 15Let Consider the following statements: 1. is increasing in the interval 2. is decreasing in the interval 3. Which of the statements given ab2024 (Phase 1)Monotonicity
  16. 16Let Consider the following statements: 1. 2. attains local minimum value at 3. A local minimum value of is Which of the statements given abo2024 (Phase 1)Maxima Minima
  17. 17A differentiable function has a local maximum at . Let . Which of the following is/are correct? 1. 2. Select the correct answer using the co2024 (Phase 1)Maxima Minima
  18. 18A differentiable function has a local maximum at . Let . The function has a relative maxima at for2024 (Phase 1)Maxima Minima
  19. 19Paragraph: Let on Question: What is the greatest value of ?2024 (Phase 2)Maxima Minima
  20. 20Paragraph: Let on Question: What is the least value of ?2024 (Phase 2)Maxima Minima
  21. 21Paragraph: Let where Question: What is the minimum value of ?2023 (Phase 1)Maxima Minima
  22. 22Paragraph: Let where Question: At what value of does attain the minimum value?2023 (Phase 1)Maxima Minima
  23. 23Paragraph: Given that , where is a fixed positive real number. Question: Under what condition does attain the least value?2023 (Phase 1)Maxima Minima
  24. 24Consider the following statements: 1. is increasing in 2. is decreasing in Which of the statements given above is/are correct?2023 (Phase 1)Monotonicity
  25. 25A function is defined by The function is decreasing on:2023 (Phase 2)Monotonicity
  26. 26A function is defined by The function attains local minimum value at:2023 (Phase 2)Maxima Minima
  27. 27Given that What is the maximum value of xy?2023 (Phase 2)Maxima Minima
  28. 28Let . What is the greatest value of the function?2023 (Phase 2)Maxima Minima
  29. 29How many extreme values does , where have?2022 (Phase 1)Maxima Minima
  30. 30In which one of the following intervals is the function decreasing?2022 (Phase 1)Monotonicity
  31. 31If the derivative of the function vanishes at , then what is the value of2022 (Phase 1)Maxima Minima
  32. 32Let be a function such that and . Let . Then consider the following statements : 1. 2. Which of the statements given above is/are correct?2022 (Phase 2)Rate Measure Error and Approximation
  33. 33Under which one of the following conditions does the function attain minimum value?2022 (Phase 2)Maxima Minima
  34. 34Where does the function attain its minimum value2022 (Phase 2)Maxima Minima
  35. 35The curve has the maximum slope at2021 (Phase 1)Maxima Minima
  36. 36A 24 cm long wire is bent to form a triangle with one of the angles as . What is the altitude of the triangle having the greatest possible a2021 (Phase 1)Maxima Minima
  37. 37Consider the following statements in respect of the function : 1. increases in the interval . 2. decreases in the interval . Which of the ab2021 (Phase 1)Monotonicity
  38. 38For what value of , where , does attain maximum value?2021 (Phase 2)Maxima Minima
  39. 39Consider the following statements in respect of the function : 1. The local maximum value of is less than its local minimum value. 2. The lo2021 (Phase 2)Maxima Minima
  40. 40What is the maximum area of a rectangle that can be inscribed in a circle of radius 2 units?2021 (Phase 2)Maxima Minima
  41. 41What is the condition that has no local extremum?2021 (Phase 2)Monotonicity
  42. 42If the function is monotonically increasing in the interval , then which one of the following is correct?2021 (Phase 2)Monotonicity
  43. 43The tangent to the curve at makes an angle with the positive direction of -axis. Which one of the following is correct?2021 (Phase 2)Tangent Normal
  44. 44Consider the following statements in respect of the function in the interval . 1. The maximum value of the function is 5 . 2. The minimum va2021 (Phase 2)Maxima Minima
  45. 45Where does the tangent to the curve at the point meet -axis?2021 (Phase 2)Tangent Normal
  46. 46Consider the following statements : 1. The function increases in the interval . 2. The function increases in the interval . Which of the abo2020Monotonicity
  47. 47Let be the length and be the breadth of a rectangle such that . What is the maximum area of the rectangle?2020Maxima Minima
  48. 48Let . If changes from 10 to 10.1 , then what is the total change in ?2020Rate Measure Error and Approximation
  49. 49The radius of a circle is increasing at the rate of . What is the rate of increase of its circumference?2020Rate Measure Error and Approximation
  50. 50A given quantity of metal is to be cast into a half cylinder (i,e, with a rectangular base and semicircular ends). If the total surface area2019 (Phase 1)Maxima Minima

Frequently Asked Questions

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

This chapter includes 140 questions compiled from NDA papers spanning 2010 to 2026.

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

These are NDA 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 NDA Mathematics?

Application of Derivatives has appeared in 17 of the 17 years of NDA papers covered here, with 140 questions across 32 papers - about 4 per paper it appears in.

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

Of the 140 questions analysed for this chapter, 16% are easy, 80% moderate and 4% tough. 2014 had the most, with 13 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 - 68 questions (49%)
  • Monotonicity - 44 questions (31%)
  • Tangent Normal - 15 questions (11%)
  • Maxima Minima has produced the most tough questions (3).
6.Is Application of Derivatives's weightage in NDA going up or down?

Across all 32 papers analysed, Application of Derivatives has averaged about 4.4 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 4.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.