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Mathematics - Application of Derivatives

Practise 47 Manipal (MET) previous year questions on Application of Derivatives, compiled from papers spanning 2010 to 2021. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty Manipal (MET) tests.

Application of Derivatives has been asked in 12 of the 15 years of Manipal (MET) papers analysed (2010–2024), with 47 questions in all. 45% of them were easy, 38% moderate and 17% tough. Most of its questions came from 2014, with 8 questions that year.

The chapter's 5 topics are not weighted equally: Maxima Minima (19 questions, 40%), Rate Measure Error and Approximation (10 questions, 21%), and Tangent Normal (10 questions, 21%) have been asked the most. Maxima Minima has also led over the last five years, with 2 questions. Tangent Normal has produced the most tough questions (4).

  1. 1The function has maximum value, when is equal to2021Maxima Minima
  2. 2If and , then is increasing in2020Monotonicity
  3. 3The curve, for which the area of the triangle formed by -axis, the tangent line at any poin and line is equal to , is given by2020Tangent Normal
  4. 4The radius of a cylinder is increasing at the rate of and its height is decreasing at the rate of . When the radius is 3 m and height is 5 m2020Rate Measure Error and Approximation
  5. 5The values of , if increases , are in2020Monotonicity
  6. 6By Newton-Raphson method, the positive root of the equation is2020Rate Measure Error and Approximation
  7. 7If , then the equation has atleast one real root in2020Mean Value Theorem
  8. 8If , then has2020Maxima Minima
  9. 9A function is2019Monotonicity
  10. 10The minimum value of is, at2018Maxima Minima
  11. 11The value of ' ' for which the function has an extremum at , is2018Maxima Minima
  12. 12The function has maximum value, when is equal to2018Maxima Minima
  13. 13If the rate of change in the circumference of a circle of , then the rate of change in the area of the circle when the radius is 5 cm , is2018Rate Measure Error and Approximation
  14. 14The minimum value of is equal to2018Maxima Minima
  15. 15The equation of the tangent to the curve , where it crosses the -axis, is2017Tangent Normal
  16. 16The function is maximum when is equal to2017Maxima Minima
  17. 17If , then the maximum value of is2016Maxima Minima
  18. 18The points on the curve which are nearest to the origin, are2016Tangent Normal
  19. 19Let , for every real numbers . Then,2016Maxima Minima
  20. 20If , then is equal to2016Rate Measure Error and Approximation
  21. 21If , then the minimum value of is2016Maxima Minima
  22. 22If is the semi-vertical angle of a cone of maximum volume and given slant height, then is given by2016Rate Measure Error and Approximation
  23. 23The number of values of , where attains its maximum is2016Maxima Minima
  24. 24The approximate value of is2015Rate Measure Error and Approximation
  25. 25The value of prescribed by Lagrange's mean value theorem, when and , is2015Mean Value Theorem
  26. 26If , then is2015Monotonicity
  27. 27The equation of the tangent to the curve at the point of its maximum, is2015Tangent Normal
  28. 28The two tangents to the curve at the points, where it crosses -axis, are2015Tangent Normal
  29. 29The greatest value of the function in , is2015Maxima Minima
  30. 30A cone whose height is always equal to its diameter, is increasing in volume at the rate of . At what rate is the radius increasing when its2015Rate Measure Error and Approximation
  31. 31The function is increasing, when2014Monotonicity
  32. 32The triangle formed by the tangent to the curve at the point and the coordinate axes lies in the first quadrant. If its area is 2 , then the2014Tangent Normal
  33. 33The equation of the tangent to the curve at is2014Tangent Normal
  34. 34The largest term in the sequence is given by2014Maxima Minima
  35. 35The number of points, where attains its minimum value, is2014Maxima Minima
  36. 36The approximate value of , where , is2014Rate Measure Error and Approximation
  37. 37What are the values of for which Rolle's theorem for the function in the interval is verified?2014Mean Value Theorem
  38. 38The minimum value of is2014Maxima Minima
  39. 39A man 1.6 m high walks at the rate of away from a lamp which is 4 m above ground. How fast is the man's shadow lengthening?2013Rate Measure Error and Approximation
  40. 40The value such that the length of subtangent and subnormal is equal for the curve at the point is2013Tangent Normal
  41. 41is a diameter of a circle and is any point on the circumference of the circle. then2013Maxima Minima
  42. 42If an edge of a cube measure 2 m with a possible error of 0.5 cm . Find the corresponding error in the calculated volume of the cube2012Rate Measure Error and Approximation
  43. 43Local maximum value of the function is2012Maxima Minima
  44. 44Let be any point on the curve . Then, the length of the segment of the tangent between the coordinate axes of length2012Tangent Normal
  45. 45The two curves and2011Tangent Normal
  46. 46The point in the interval , where has maximum slope, is2010Maxima Minima
  47. 47The function has a local maxima at , then2010Maxima Minima

Frequently Asked Questions

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

This chapter includes 47 questions compiled from Manipal (MET) papers spanning 2010 to 2021.

2.Are these questions only from Manipal (MET), or from other exams too?

These are Manipal (MET) 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 Manipal (MET) Mathematics?

Application of Derivatives has appeared in 12 of the 15 years of Manipal (MET) papers covered here, with 47 questions across 12 papers - about 4 per paper it appears in.

4.What is the difficulty level of Application of Derivatives questions in Manipal (MET)?

Of the 47 questions analysed for this chapter, 45% are easy, 38% moderate and 17% tough. 2014 had the most, with 8 questions.

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

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

  • Maxima Minima - 19 questions (40%)
  • Rate Measure Error and Approximation - 10 questions (21%)
  • Tangent Normal - 10 questions (21%)
  • Tangent Normal has produced the most tough questions (4).