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Mathematics - Application of Derivatives

Practise 22 NEST (NISER) previous year questions on Application of Derivatives, compiled from papers spanning 2012 to 2023. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NEST (NISER) tests.

Application of Derivatives has been asked in 9 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 22 questions in all. 5% of them were easy, 68% moderate and 27% tough. Most of its questions came from 2023, with 5 questions that year. In the last three years (2024–2026) it had 0 questions across 4 papers, about 0 per paper.

The chapter's 4 topics are not weighted equally: Monotonicity (16 questions, 73%), Maxima Minima (3 questions, 14%), and Mean Value Theorem (2 questions, 9%) have been asked the most. Monotonicity has also led over the last five years, with 7 questions. Monotonicity has produced the most tough questions (5).

  1. 1Let be a differentiable function such that for all . Then2023 (Session 1)Monotonicity
  2. 2Let be a differentiable function such that for all . Then2023 (Session 1)Monotonicity
  3. 3Let be the function on defined by , where . Then the set of all possible values of for which is strictly increasing is2023 (Session 2)Monotonicity
  4. 4For , with , let denote the number of elements in the set . Then2023 (Session 2)Monotonicity
  5. 5Let for all . Then the number of points at which the graph of cuts the axis is2023 (Session 2)Monotonicity
  6. 6The number of solutions of is2022 (Session 1)Monotonicity
  7. 7Let and be non-negative real numbers satisfying . Then the minimum value of is2022 (Session 1)Monotonicity
  8. 8A continuous function is said to be good if given , the line segment joining the points and lies on or above the graph of in the interval . 2021 (Session 1)Monotonicity
  9. 9Let be a twice differentiable function on such that Here, and denote the first and second order derivative of at respectively. Then2020 (Session 1)Mean Value Theorem
  10. 10Let be a nonconstant differentiable function such that and for some . Then2020 (Session 1)Monotonicity
  11. 11Let be a polynomial whose coefficients are real numbers. Suppose the roots of are real. Then2020 (Session 1)Monotonicity
  12. 12Consider the equations and The number of values of for which the above two equations intersect at exactly two points is2020 (Session 2)Monotonicity
  13. 13Let be a differentiable function such that . Then2020 (Session 2)Mean Value Theorem
  14. 14Let be a function defined as . Then2019 (Session 1)Monotonicity
  15. 15Let positive real numbers and be such that . The maximum value of is2016Maxima Minima
  16. 16The number of real solutions of is2016Monotonicity
  17. 17For a given positive integer let be defined as Then2016Maxima Minima
  18. 18The set of all real numbers on which the function is strictly increasing is:2015Monotonicity
  19. 19Let be the set of all real numbers and be a differentiable function satisfying . If the graph of passes through the origin then2015Limits
  20. 20Consider a function defined over positive real numbers. Which of the following statements is/are true?2014Monotonicity
  21. 21Let and be two functions. Then2014Monotonicity
  22. 22Let be points on the same side of a straight line in a plane. Suppose P is a point on such that is the minimum. Then2012Maxima Minima

Frequently Asked Questions

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

This chapter includes 22 questions compiled from NEST (NISER) papers spanning 2012 to 2023.

2.Are these questions only from NEST (NISER), or from other exams too?

These are NEST (NISER) 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 NEST (NISER) Mathematics?

Application of Derivatives has appeared in 9 of the 16 years of NEST (NISER) papers covered here, with 22 questions across 11 papers - about 2 per paper it appears in.

4.What is the difficulty level of Application of Derivatives questions in NEST (NISER)?

Of the 22 questions analysed for this chapter, 5% are easy, 68% moderate and 27% tough. 2023 had the most, with 5 questions.

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

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

  • Monotonicity - 16 questions (73%)
  • Maxima Minima - 3 questions (14%)
  • Mean Value Theorem - 2 questions (9%)
  • Monotonicity has produced the most tough questions (5).
6.Is Application of Derivatives's weightage in NEST (NISER) going up or down?

Across all 11 papers analysed, Application of Derivatives has averaged about 2.0 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.