Jump to a section

Mathematics - Application of Derivatives

Practise 348 AP EAMCET previous year questions on Application of Derivatives, compiled from papers spanning 2001 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty AP EAMCET tests.

Application of Derivatives has been asked in 24 of the 24 years of AP EAMCET papers analysed (2001–2024), with 348 questions in all. 45% of them were easy, 46% moderate and 10% tough. Most of its questions came from 2021, with 47 questions that year. In the last three years (2022–2024) it had 115 questions across 28 papers, about 4.1 per paper.

The chapter's 5 topics are not weighted equally: Tangent Normal (125 questions, 36%), Maxima Minima (100 questions, 29%), and Rate Measure Error and Approximation (57 questions, 16%) have been asked the most. Tangent Normal has also led over the last five years, with 79 questions. Maxima Minima has produced the most tough questions (15).

  1. 1Consider the quadratic equation , where and let . Statement-I : The given quadratic equation has at least one root in . Statement-II : Rolle27 May, 2025 (M)Mean Value Theorem
  2. 2The difference between the absolute maximum and absolute minimum values of the function on is27 May, 2025 (M)Maxima Minima
  3. 3If , then is27 May, 2025 (M)Monotonicity
  4. 4The angle between the curves and at the point is27 May, 2025 (M)Tangent Normal
  5. 5If the tangent of the curve drawn at the point forms a triangle of area sq.units with the coordinate axes then26 May, 2025 (M)Tangent Normal
  6. 6If the function is defined on the interval , then is strictly increasing in the interval26 May, 2025 (M)Monotonicity
  7. 7If the Lagrange's mean value theorem is applied to the function defined on the interval and the value of is , then26 May, 2025 (M)Mean Value Theorem
  8. 8If the tangent to the curve at makes an angle with X -axis, then26 May, 2025 (E)Tangent Normal
  9. 9If the displacement of a particle travelling along a straight line in seconds is given by , then the time taken (in seconds) by the particle26 May, 2025 (E)Rate Measure Error and Approximation
  10. 10If the function satisfies all the conditions of Rolle's theorem in and , then26 May, 2025 (E)Mean Value Theorem
  11. 11If the surface area of a spherical bubble is increasing at the rate of , then the rate of change in its volume (in cubic ) when its radius i24 May, 2025 (M)Rate Measure Error and Approximation
  12. 12The number of turning points of the curve in the interval is24 May, 2025 (M)Maxima Minima
  13. 13The radius and the height of a right circular solid cone are measured as 7 feet each. If there is an error of 0.002 ft for every feet in mea24 May, 2025 (M)Rate Measure Error and Approximation
  14. 14Let be such that is the only real root of . If , then in the interval23 May, 2025 (M)Maxima Minima
  15. 15If the volume of a sphere is increasing at the rate of , then the rate (in ) at which its surface area is increasing, when the diameter of t23 May, 2025 (M)Rate Measure Error and Approximation
  16. 16If the lengths of the tangent, subtangent, normal and subnormal for the curve at the point are and respectively, then their increasing order23 May, 2025 (M)Tangent Normal
  17. 17The slope of a tangent drawn at the point lying on the curve is -2. If P lies in the fourth quadrant, then23 May, 2025 (E)Tangent Normal
  18. 18The function attains a maximum value at , then23 May, 2025 (E)Maxima Minima
  19. 19If m and M are the absolute minimum and absolute maximum values of the function in the interval , then23 May, 2025 (E)Maxima Minima
  20. 20If the tangent drawn at the point on the curve is parallel to the line , then22 May, 2025 (M)Tangent Normal
  21. 21The displacement S of a particle measured from a fixed point O on a line is given by . Then the time at which displacement of the particle i22 May, 2025 (M)Maxima Minima
  22. 22If the extreme value of the function in is and it exists at , then22 May, 2025 (M)Maxima Minima
  23. 23The interval in which the curve represented by is increasing is22 May, 2025 (M)Monotonicity
  24. 24If the tangent drawn at the point on the curve passes through origin, then22 May, 2025 (E)Tangent Normal
  25. 25Which one of the following functions is monotonically increasing in its domain?22 May, 2025 (E)Monotonicity
  26. 26If is an angle between the normals drawn to the curve at the points and , then22 May, 2025 (E)Tangent Normal
  27. 27If the area of a right angled triangle with hypotenuse 5 is maximum, then its perimeter is22 May, 2025 (E)Maxima Minima
  28. 28The area (in square units) of the triangle formed by the X - axis, the tangent and the normal drawn at to the curve is21 May, 2025 (M)Tangent Normal
  29. 29The value c of the Rolle's theorem for the function in the interval is21 May, 2025 (M)Mean Value Theorem
  30. 30If the function representing the slopes of the tangents drawn to the curve is strictly increasing then the domain of is21 May, 2025 (M)Monotonicity
  31. 31If the normal drawn at the point on the curve is parallel to the line , then21 May, 2025 (E)Tangent Normal
  32. 32If the curves and intersect at right angles, then21 May, 2025 (E)Tangent Normal
  33. 33If the function is defined in the interval , then is strictly increasing in the interval21 May, 2025 (E)Monotonicity
  34. 34If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its acceleration is21 May, 2025 (E)Rate Measure Error and Approximation
  35. 35A is a point on the circle with radius 8 and centre at . A particle P is moving on the circumference of the circle starting from A. M. is th23 May, 2024 (M)Rate Measure Error and Approximation
  36. 36If the length of the sub-tangent at any point on a curve is proportional to the abscissa of the point P. then the equation of that curve is 23 May, 2024 (M)Tangent Normal
  37. 37In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which23 May, 2024 (M)Mean Value Theorem
  38. 38The value of Lagrange's mean value theorem for in is22 May, 2024 (M)Mean Value Theorem
  39. 39Equation of the normal to the curve at the point is22 May, 2024 (M)Tangent Normal
  40. 40Displacement of a particle at time is expressed as . Find the acceleration at the time when the velocity vanishes.22 May, 2024 (M)Rate Measure Error and Approximation
  41. 41If a running track of 500 ft . is to be laid out enclosing a playground, the shape of which is a rectangle with a semicircle at each end, th22 May, 2024 (M)Maxima Minima
  42. 42The semi-vertical angle of a right circular cone is . If the radius of the base of the cone is measured as 14 cm with an error of , then the22 May, 2024 (E)Rate Measure Error and Approximation
  43. 43If a man of height 1.8 mt . is walking away from the foot of a light pole of height 6 mt . with a speed of 7 km per hour on a straight horiz22 May, 2024 (E)Rate Measure Error and Approximation
  44. 44If the curves and cut each other orthogonally, then22 May, 2024 (E)Tangent Normal
  45. 45The interval containing all the real values of such that the real valued function is strictly increasing is22 May, 2024 (E)Monotonicity
  46. 46If a number is drawn at random from the set , , then the probability that it lies in the interval in which the function is strictly decreasi21 May, 2024 (M)Monotonicity
  47. 47The point which lies on the tangent drawn to the curve at the point is21 May, 2024 (M)Tangent Normal
  48. 48If , then the interval in which decreases is21 May, 2024 (M)Monotonicity
  49. 49If the Rolle's theorem is applicable for the function defined by on , then the value of C of the Rolle's theorem is21 May, 2024 (M)Mean Value Theorem
  50. 50The number of all the values of for which the function attains its maximum value on is21 May, 2024 (M)Maxima Minima

Frequently Asked Questions

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

This chapter includes 348 questions compiled from AP EAMCET papers spanning 2001 to 2025.

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

These are AP EAMCET 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 AP EAMCET Mathematics?

Application of Derivatives has appeared in 25 of the 25 years of AP EAMCET papers covered here, with 348 questions across 93 papers - about 4 per paper it appears in.

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

Of the 348 questions analysed for this chapter, 45% are easy, 46% moderate and 10% tough. 2021 had the most, with 47 questions.

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

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

  • Tangent Normal - 125 questions (36%)
  • Maxima Minima - 100 questions (29%)
  • Rate Measure Error and Approximation - 57 questions (16%)
  • Maxima Minima has produced the most tough questions (15).
6.Is Application of Derivatives's weightage in AP EAMCET going up or down?

Across all 93 papers analysed, Application of Derivatives has averaged about 3.7 questions per paper. In the last three years (2022–2024), that average has stayed about the same, at about 4.1 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.