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Mathematics - Application of Derivatives

Practise 372 MHTCET previous year questions on Application of Derivatives, compiled from papers spanning 2007 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 MHTCET tests.

Application of Derivatives has been asked in 17 of the 17 years of MHTCET papers analysed (2007–2026), with 372 questions in all. 40% of them were easy, 51% moderate and 9% tough. Most of its questions came from 2024, with 69 questions that year. In the last three years (2024–2026) it had 180 questions across 59 papers, about 3.1 per paper.

The chapter's 5 topics are not weighted equally: Rate Measure Error and Approximation (109 questions, 29%), Tangent Normal (103 questions, 28%), and Maxima Minima (80 questions, 22%) have been asked the most. Rate Measure Error and Approximation has also led over the last five years, with 79 questions. Tangent Normal has produced the most tough questions (11).

  1. 1On the interval , the function attains its maximum value at the point ....20 Apr, 2026 (M)Maxima Minima
  2. 2If the line is a normal to the curve then .....20 Apr, 2026 (M)Tangent Normal
  3. 3A spherical iron ball cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of . When the thickness of ice is20 Apr, 2026 (M)Rate Measure Error and Approximation
  4. 4The function satisfies all the conditions of Rolle's theorem in , then20 Apr, 2026 (E)Mean Value Theorem
  5. 5The line touches the curve at then values of and respectively are ...........20 Apr, 2026 (E)Tangent Normal
  6. 6An aeroplane at an altitude of 1 km is flying horizontally at 600 km / hr, passes directly over an observer. Then the rate at which it is ap20 Apr, 2026 (E)Rate Measure Error and Approximation
  7. 7The value of satisfied by the Rolle's theorem for the function , is...19 Apr, 2026 (M)Mean Value Theorem
  8. 8A particle is fired straight up from the ground. Its height in feet after second is given by . The velocity of the particle when it hits the19 Apr, 2026 (M)Rate Measure Error and Approximation
  9. 9A tank with a rectangular base and rectangular sides, open at the top is made. Depth of the tank is m and its volume is cubic meters. For ma19 Apr, 2026 (M)Maxima Minima
  10. 10If the rate of increase of surface area of a spherical balloon is and rate of increase of volume of a spherical balloon is , then the radius19 Apr, 2026 (E)Rate Measure Error and Approximation
  11. 11Rolle's theorem holds for monic quadratic polynomial on the interval where . Similarly, also follows Rolle's theorem in the interval where ,19 Apr, 2026 (E)Mean Value Theorem
  12. 12If the side of an equilateral triangle increases at the rate of , then the rate of change of increase of its area when the side is is ____18 Apr, 2026 (M)Rate Measure Error and Approximation
  13. 13If the tangent to the curve at makes an angle of with positive direction of the -axis, then the value of is...18 Apr, 2026 (M)Tangent Normal
  14. 14If the line is the normal to the curve given by , , (where ) at a point , then18 Apr, 2026 (M)Tangent Normal
  15. 15If a particle moves such that the displacement (s) is proportional to the square of the velocity (v), then its acceleration (a) is18 Apr, 2026 (E)Rate Measure Error and Approximation
  16. 16If the function satisfies all the conditions of Rolle's theorem on and the slope of the tangent to the curve at is zero, then18 Apr, 2026 (E)Mean Value Theorem
  17. 17Let and , then18 Apr, 2026 (E)Monotonicity
  18. 18The number 28 is divided into two positive parts such that the sum of the cube of one part and the square of the other part is minimum, then17 Apr, 2026 (M)Maxima Minima
  19. 19If , then the values of for which is monotonically increasing and monotonically decreasing are respectively.....17 Apr, 2026 (M)Monotonicity
  20. 20The function , then is17 Apr, 2026 (M)Monotonicity
  21. 21The tangent to the curve intersects the Y-axis at point P. A line drawn through point P is perpendicular to this tangent and passes through 17 Apr, 2026 (M)Tangent Normal
  22. 22If the line is tangent to the curve at the point , then the value of is...17 Apr, 2026 (E)Tangent Normal
  23. 23The equation of the tangent to the curve at the point where the ordinate and abscissa equal is...17 Apr, 2026 (E)Tangent Normal
  24. 24The coordinates of the points on the curve that are nearest to the point are ...17 Apr, 2026 (E)Maxima Minima
  25. 25The minimum value of in the interval is16 Apr, 2026 (M)Maxima Minima
  26. 26The function is an increasing function in the interval.....16 Apr, 2026 (M)Monotonicity
  27. 27A triangle has two fixed vertices A and B . Let its third vertex C is moving along the line . If is the area of triangle ABC, then16 Apr, 2026 (M)Rate Measure Error and Approximation
  28. 28The equation of tangent to the curves and at the point is...16 Apr, 2026 (E)Tangent Normal
  29. 29A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius when the radiu16 Apr, 2026 (E)Rate Measure Error and Approximation
  30. 30A cylindrical tank without a top lid is being manufactured to hold a fixed volume of cubic cm. The minimum surface area required to construc16 Apr, 2026 (E)Maxima Minima
  31. 31The co-ordinates of the point on the curve at which the normal is parallel to the line are...15 Apr, 2026 (M)Tangent Normal
  32. 32If the function satisfies Roll's theorem in , if then is equal to...15 Apr, 2026 (M)Mean Value Theorem
  33. 33A spherical mothball has initial radius 3 cm. Due to evaporation, the radius of the ball reduces to 1 cm in 4 months. In how many months wou15 Apr, 2026 (E)Rate Measure Error and Approximation
  34. 34The point on the curve where the normal to the curve makes equal intercepts with the co-ordinate axes is15 Apr, 2026 (E)Tangent Normal
  35. 35The maximum value of , is15 Apr, 2026 (E)Maxima Minima
  36. 36The surface area of a spherical ball is increasing at the rate of /second. The rate at which the radius is increasing when the surface area 15 Apr, 2026 (E)Rate Measure Error and Approximation
  37. 37If a spherical balloon has a variable diameter units, then the rate of change of its volume with respect to is13 Apr, 2026 (M)Rate Measure Error and Approximation
  38. 38A wire 40 metre in length is to be cut into two pieces. One piece is formed into a square and the other piece into a circle. The lengths of 13 Apr, 2026 (M)Maxima Minima
  39. 39The equation of the normal to the curve is , then13 Apr, 2026 (M)Tangent Normal
  40. 40Let be the differentiable function for all such that and . The maximum value of is...13 Apr, 2026 (E)Mean Value Theorem
  41. 41If the tangent to the curve at the point cuts off intercepts and on the coordinate axes such that , then the value of is13 Apr, 2026 (E)Tangent Normal
  42. 42If Rolle's theorem is applicable for the function on with such that , then the value of is13 Apr, 2026 (E)Mean Value Theorem
  43. 43The equation of the tangent to the curve at is11 Apr, 2026 (M)Tangent Normal
  44. 44The approximate value of is11 Apr, 2026 (M)Rate Measure Error and Approximation
  45. 45A wire of length m is to be bent to form a rectangle such that its area is maximum, then its area is.....11 Apr, 2026 (M)Maxima Minima
  46. 46The difference between the local extreme values of the function is ......11 Apr, 2026 (M)Maxima Minima
  47. 47The value of such that the function is strictly decreasing for all real is11 Apr, 2026 (E)Monotonicity
  48. 48The tangent to the curve is vertical when11 Apr, 2026 (E)Tangent Normal
  49. 49If the function , defined on , satisfies all the conditions of Rolle's theorem for , then11 Apr, 2026 (E)Mean Value Theorem
  50. 50The area of the triangle formed by the co-ordinate axes and a tangent to the curve at the point is ________ sq.units (where and are non zero05 May, 2025 (E)Tangent Normal

Frequently Asked Questions

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

This chapter includes 372 questions compiled from MHTCET papers spanning 2007 to 2026.

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

These are MHTCET 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 MHTCET Mathematics?

Application of Derivatives has appeared in 17 of the 17 years of MHTCET papers covered here, with 372 questions across 107 papers - about 3 per paper it appears in.

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

Of the 372 questions analysed for this chapter, 40% are easy, 51% moderate and 9% tough. 2024 had the most, with 69 questions.

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

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

  • Rate Measure Error and Approximation - 109 questions (29%)
  • Tangent Normal - 103 questions (28%)
  • Maxima Minima - 80 questions (22%)
  • Tangent Normal has produced the most tough questions (11).
6.Is Application of Derivatives's weightage in MHTCET going up or down?

Across all 107 papers analysed, Application of Derivatives has averaged about 3.5 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 3.1 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.