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Mathematics - Application of Derivatives

Practise 229 TS 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 TS EAMCET tests.

Application of Derivatives has been asked in 24 of the 24 years of TS EAMCET papers analysed (2001–2024), with 229 questions in all. 52% of them were easy, 40% moderate and 8% tough. Most of its questions came from 2024, with 29 questions that year. In the last three years (2022–2024) it had 64 questions across 17 papers, about 3.8 per paper.

The chapter's 6 topics are not weighted equally: Tangent Normal (79 questions, 34%), Rate Measure Error and Approximation (61 questions, 27%), and Maxima Minima (55 questions, 24%) have been asked the most. Tangent Normal has also led over the last five years, with 40 questions. Rate Measure Error and Approximation has produced the most tough questions (8).

  1. 1If the curves and cut each other orthogonally then the length of the sub tangent at on the curve is04 May, 2025 (M)Tangent Normal
  2. 2A rod of length 41 m with an end on the floor and another end on the wall perpendicular to the floor is sliding away horizontally from the w04 May, 2025 (M)Rate Measure Error and Approximation
  3. 3There is a possible error of 0.02 cm in measuring the base diameter of a right circular cone as 14 cm. If the semi-vertical angle of the con04 May, 2025 (M)Rate Measure Error and Approximation
  4. 4The real valued function is04 May, 2025 (M)Monotonicity
  5. 5If and are two positive real numbers such that then the minimum value of is04 May, 2025 (M)Maxima Minima
  6. 6If local maximum of exists at , then04 May, 2025 (E)Maxima Minima
  7. 7If and at , then04 May, 2025 (E)Parametric differentiation
  8. 8For the curve the line is04 May, 2025 (E)Tangent Normal
  9. 9The height of a cone with semi vertical angle is increasing at the rate of 2 units . The rate at which the radius of the cone is to be decre04 May, 2025 (E)Rate Measure Error and Approximation
  10. 10The function where attains its local maximum and local minimum at and respectively. If then04 May, 2025 (E)Maxima Minima
  11. 11Consider all functions given in List-I in the interval . The List- 2 has the values of ' ' obtained by applying Lagrange's mean value theore04 May, 2025 (E)Mean Value Theorem
  12. 12If the percentage error in the radius of a circle is 3, then the percentage error in its area is04 May, 2025 (E)Rate Measure Error and Approximation
  13. 13If the normal drawn at the point P on the curve makes equal intercepts on the coordinate axes, then the equation of the tangent drawn to the03 May, 2025 (M)Tangent Normal
  14. 14If a balloon lying at an altitude of 30 m from an observer at a particular instant is moving horizontally at the rate of away from him, then03 May, 2025 (M)Rate Measure Error and Approximation
  15. 15A real valued function is defined as , then is03 May, 2025 (M)Monotonicity
  16. 16If the tangent and the normal drawn to the curve at the point meet the X -axis in T and N respectively, then03 May, 2025 (E)Tangent Normal
  17. 17A man of 5 feet height is walking away from a light fixed at a height of 15 feet at the rate of K miles/hour. If the rate of increase of his03 May, 2025 (E)Rate Measure Error and Approximation
  18. 18There is a possible error of 0.03 cm in a scale of length 1 foot with which the height of a closed right circular cylinder and the diameter 03 May, 2025 (E)Rate Measure Error and Approximation
  19. 19For a real number ' ', if a real valued function is monotonic in its domain, then the range of ' ' is03 May, 2025 (E)Monotonicity
  20. 20If the point lying on the curve is the closest point to the line then the perpendicular distance from P to the line is03 May, 2025 (E)Tangent Normal
  21. 21A variable straight-line with negative slope passes through the point and cuts the positive coordinate axes in A and B. If O is the origin, 02 May, 2025 (M)Maxima Minima
  22. 22The acute angle between the curves and at their point of intersection which lies in the first quadrant is02 May, 2025 (M)Tangent Normal
  23. 23If the rate of change of the slope of the tangent drawn to the curve at the point is k times the rate of change of its abscissa, then02 May, 2025 (M)Rate Measure Error and Approximation
  24. 24If is a well-defined real valued function then is02 May, 2025 (M)Monotonicity
  25. 25A real valued function is defined on . If m and M are absolute minimum and absolute maximum values of respectively then02 May, 2025 (M)Maxima Minima
  26. 26The radius of a cone of height 9 units is changed from 2 units to 2.12 units. The exact change and approximate change in the volume of the c02 May, 2025 (E)Rate Measure Error and Approximation
  27. 27The local maximum value and local minimum value of in exist at respectively, then02 May, 2025 (E)Maxima Minima
  28. 28is a point on the curve and is the slope of the tangent to the curve at P. The area of the triangle (in sq. units) formed by the tangent and02 May, 2025 (E)Tangent Normal
  29. 29If a particle is moving in a straight line so that after seconds its distance S (in cms ) from a fixed point on the line is given by then th02 May, 2025 (E)Rate Measure Error and Approximation
  30. 30If is a continuous and strictly increasing function, then is02 May, 2025 (E)Mean Value Theorem
  31. 31For a given function denotes the actual error in corresponding to actual error in and denotes the approximate value of . If and , then the v11 May, 2024 (M)Rate Measure Error and Approximation
  32. 32The length of the normal drawn at on the curve is11 May, 2024 (M)Tangent Normal
  33. 33If water is poured into a cylindrical tank of radius 3.5 ft at the rate of , then the rate at which the level of the water in the tank incre11 May, 2024 (M)Rate Measure Error and Approximation
  34. 34is a function defined on . If the tangent drawn at a point on the graph of this function is parallel to -axis and , then11 May, 2024 (M)Tangent Normal
  35. 35If and are respectively the absolute minimum and absolute maximum values of a function defined on , then11 May, 2024 (M)Maxima Minima
  36. 36The approximate value of obtained by taking 0.0174 and is10 May, 2024 (M)Rate Measure Error and Approximation
  37. 37The equation of the normal drawn to the curve at the point is10 May, 2024 (M)Tangent Normal
  38. 38A point P is moving on the curve . The -coordinate of is decreasing at the rate of 8 units per second. When the point is at , the -coordinat10 May, 2024 (M)Rate Measure Error and Approximation
  39. 39If the function satisfies the conditions of Rolle's theorem on the interval and are two roots of the equation , then one of the values of c 10 May, 2024 (M)Mean Value Theorem
  40. 40If and are two positive integers such that and is maximum, then10 May, 2024 (M)Maxima Minima
  41. 41The maximum interval in which the slopes of the tangents drawn to the curve increase is10 May, 2024 (E)Tangent Normal
  42. 42If the tangent drawn at to the curve is a horizontal line and the tangent drawn at Q to the curve is a vertical line \} then10 May, 2024 (E)Tangent Normal
  43. 43In a , the sides are fixed. In measuring angle , if there is an error of , then the percentage error in measuring the length of the side is10 May, 2024 (E)Rate Measure Error and Approximation
  44. 44and are two curves and is a common point of the two curves. If at , on the curve and at the same point on the curve , then10 May, 2024 (E)Tangent Normal
  45. 45If Rolle's Theorem is applicable for the function on the interval , then a possible value of is10 May, 2024 (E)Mean Value Theorem
  46. 46The sum of the maximum and minimum values of the function is10 May, 2024 (E)Maxima Minima
  47. 47The radius of a sphere is 7 cm . If an error of . is made in measuring it, then the approximate error (in cubic cm ) found in its volume is09 May, 2024 (M)Rate Measure Error and Approximation
  48. 48The curve intersects the horizontal line at the point . If the tangent drawn to this curve at P meets the -axis at , then09 May, 2024 (M)Tangent Normal
  49. 49A particle moving from a fixed point on a straight line travels a distance metres in . If , then the distance (in mts) travelled by the part09 May, 2024 (M)Rate Measure Error and Approximation
  50. 50If is a real valued function defined on , then the value(s) of ' ' as defined in the statement of Rolle's theorem09 May, 2024 (M)Mean Value Theorem

Frequently Asked Questions

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

This chapter includes 229 questions compiled from TS EAMCET papers spanning 2001 to 2025.

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

These are TS 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 TS EAMCET Mathematics?

Application of Derivatives has appeared in 25 of the 25 years of TS EAMCET papers covered here, with 229 questions across 64 papers - about 4 per paper it appears in.

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

Of the 229 questions analysed for this chapter, 52% are easy, 40% moderate and 8% tough. 2024 had the most, with 29 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 - 79 questions (34%)
  • Rate Measure Error and Approximation - 61 questions (27%)
  • Maxima Minima - 55 questions (24%)
  • Rate Measure Error and Approximation has produced the most tough questions (8).
6.Is Application of Derivatives's weightage in TS EAMCET going up or down?

Across all 64 papers analysed, Application of Derivatives has averaged about 3.6 questions per paper. In the last three years (2022–2024), that average has stayed about the same, at about 3.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.