Application of Derivatives

JEE Advanced · Mathematics · 48 past questions

1. Q1 2026 Paper 1

   Consider the function $f:(0,\infty)\to(-\infty,\infty)$ given by…

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2. Q2 2025 Paper 2

   Let $\mathbb{R}$ denote the set of all real numbers. Let $f:\mathbb{R}\to\mathbb{R}$ be defined by…

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3. Q3 2021 Paper 1

   Let $f:\mathbb{R}\to\mathbb{R}$ be defined by…

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4. Q4 2021 Paper 2

   Let $f_1:(0,\infty)\to\mathbb{R}$ and $f_2:(0,\infty)\to\mathbb{R}$ be defined by…

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5. Q5 2021 Paper 2

   Let $f_1:(0,\infty)\to\mathbb{R}$ and $f_2:(0,\infty)\to\mathbb{R}$ be defined by…

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6. Q6 2021 Paper 2

   Paragraph…

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7. Q7 2020 Paper 1

   Consider all rectangles lying in the region…

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8. Q8 2020 Paper 2

   Let the function $f:(0,\pi)\to\mathbb{R}$ be defined by…

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9. Q9 2019 Paper 1

   Let $f: \mathbb{R} \to \mathbb{R}$ be given by…

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10. Q10 2019 Paper 2

    Let $f(x) = \dfrac{\sin \pi x}{x^2}, \quad x>0.$…

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11. Q11 2019 Paper 2

    Let $f: \mathbb{R} \to \mathbb{R}$ be given by $f(x) = (x-1)(x-2)(x-5)$. Define…

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12. Q12 2018 Paper 2

    Let $f:(0,\pi)\to\mathbb{R}$ be a twice differentiable function such that…

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13. Q13 2017 Paper 1

    Answer Q.52, Q.53 and Q.54 by appropriately matching the information given in the three columns of the…

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14. Q14 2017 Paper 1

    Answer Q.52, Q.53 and Q.54 by appropriately matching the information given in the three columns of the…

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15. Q15 2017 Paper 2

    If $f:\mathbb{R}\to\mathbb{R}$ is a differentiable function such that $f'(x) > 2f(x)$ for all…

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16. Q16 2016 Paper 1

    The least value of $\alpha \in \mathbb{R}$ for which $4\alpha x^2 + \frac{1}{x} \ge 1$, for all $x > 0$, is

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17. Q17 2016 Paper 2

    Let…

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18. Q18 2015 Paper 1

    A cylindrical container is to be made from certain solid material with the following constraints: It has a…

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19. Q19 2015 Paper 2

    Let $f,g:[-1,2]\to\mathbb{R}$ be continuous functions which are twice differentiable on the interval…

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20. Q20 2014 Paper 1

    For every pair of continuous functions $f, g: [0,1] \to \mathbb{R}$ such that…

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21. Q21 2014 Paper 1

    Let $f: (0,\infty) \to \mathbb{R}$ be given by…

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22. Q22 2014 Paper 1

    Let $a \in \mathbb{R}$ and let $f: \mathbb{R} \to \mathbb{R}$ be given by…

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23. Q23 2014 Paper 1

    The slope of the tangent to the curve $(y-x^5)^2=x(1+x^2)^2$ at the point $(1,3)$ is

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24. Q24 2014 Paper 2

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25. Q25 2013 Paper 1

    Let $f(x) = x \sin \pi x$, $x > 0$. Then for all natural numbers $n$, $f'(x)$ vanishes at

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26. Q26 2013 Paper 1

    A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8:15$ is converted into…

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27. Q27 2013 Paper 2

    The function $f(x) = 2|x| + |x+2| - ||x+2| - 2|x||$ has a local minimum or a local maximum at $x =$

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28. Q28 2013 Paper 2

    Paragraph for Questions 53 and 54…

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29. Q29 2013 Paper 2

    Paragraph for Questions 53 and 54…

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30. Q30 2012 Paper 1

    Let $f:\mathbb{R}\to\mathbb{R}$ be defined as $f(x)=|x|+|x^2-1|$. The total number of points at which $f$…

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31. Q31 2012 Paper 1

    Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at…

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32. Q32 2012 Paper 2

    Paragraph for Questions 51 and 52…

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33. Q33 2010 Paper 1

    Let f, g and h be real-valued functions defined on the interval $[0,1]$ by $f(x)=e^{x^2}+e^{-x^2}$…

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34. Q34 2010 Paper 1

    Let f be a real-valued function defined on the interval $(0, \infty)$ by…

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35. Q35 2010 Paper 2

    Let $f$ be a function defined on $\mathbf{R}$ (the set of all real numbers) such that…

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36. Q36 2010 Paper 2

    Paragraph for questions 31 to 33.…

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37. Q37 2009 Paper 2

    The maximum value of the function $f(x)=2x^3-15x^2+36x-48$ on the set $A=\{x \mid x^2+20 \le 9x\}$ is

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38. Q38 2009 Paper 2

    Let $p(x)$ be a polynomial of degree 4 having extremum at $x = 1, 2$ and…

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39. Q39 2008 Paper 1

    The total number of local maxima and local minima of the function…

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40. Q40 2008 Paper 1

    Let $f(x)$ be a non-constant twice differentiable function defined on $(-\infty, \infty)$ such that…

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41. Q41 2008 Paper 2

    Let $g(x)=\log f(x)$ where $f(x)$ is a twice differentiable positive function on $(0,\infty)$ such that…

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42. Q42 2008 Paper 2

    Paragraph for Question Nos. 14 to 16…

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43. Q43 2007 Paper 1

    The tangent to the curve $y=e^x$ drawn at the point $(c, e^c)$ intersects the line joining the points…

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44. Q44 2007 Paper 1

    In the following $[x]$ denotes the greatest integer less than or equal to $x$. Match the functions in Column…

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45. Q45 2007 Paper 2

    Let $f(x) = 2 + \cos x$ for all real $x$.…

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46. Q46 2007 Paper 2

    Paragraph for Question Nos. 61 to 63…

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47. Q47 2007 Paper 2

    Paragraph for Question Nos. 61 to 63…

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48. Q48 2007 Paper 2

    Paragraph for Question Nos. 61 to 63…

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