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Mathematics - Application of Derivatives

Practise 67 BITSAT previous year questions on Application of Derivatives, compiled from papers spanning 2009 to 2024. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty BITSAT tests.

Application of Derivatives has been asked in 16 of the 16 years of BITSAT papers analysed (2009–2024), with 67 questions in all. 37% of them were easy, 52% moderate and 10% tough. Most of its questions came from 2024, with 7 questions that year. In the last three years (2022–2024) it had 14 questions across 6 papers, about 2.3 per paper.

The chapter's 5 topics are not weighted equally: Maxima Minima (22 questions, 33%), Tangent Normal (18 questions, 27%), and Monotonicity (17 questions, 25%) have been asked the most. Over the last five years the most frequent topics have been Monotonicity (7), Maxima Minima (5), and Tangent Normal (5). Maxima Minima has produced the most tough questions (2).

  1. 1The altitude of a cone is 20 cm and its semivertical angle is . If the semi-vertical angle is increasing at the rate of per second, then the2024 (Memory Based Paper 1)Rate Measure Error and Approximation
  2. 2The point of inflexion for the curve , where n is odd integer and is2024 (Memory Based Paper 1)Monotonicity
  3. 3The population at time of a certain mouse species satisfies the differential equation . If , then the time at which the population becomes z2024 (Memory Based Paper 1)Rate Measure Error and Approximation
  4. 4The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is2024 (Memory Based Paper 2)Rate Measure Error and Approximation
  5. 5If the angle made by the tangent at the point on the curve , with the positive x -axis is , then is equal to2024 (Memory Based Paper 2)Tangent Normal
  6. 6The maximum area of rectangle inscribed in a circle of diameter is2024 (Memory Based Paper 3)Maxima Minima
  7. 7Consider the function , then is2024 (Memory Based Paper 3)Monotonicity
  8. 8The interval in which the function is decreasing is :2023 (Memory Based Paper 1)Monotonicity
  9. 9The curve given by has a tangent parallel to the Y-axis at the point2023 (Memory Based Paper 1)Tangent Normal
  10. 10The function is an increasing function in2023 (Memory Based Paper 1)Monotonicity
  11. 11The function is increasing on2023 (Memory Based Paper 2)Monotonicity
  12. 12If and , then which of the following option is correct?2023 (Memory Based Paper 2)Monotonicity
  13. 13A running track of is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the ar2022Maxima Minima
  14. 14A spherical balloon is filled with cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of cubic meters2022Maxima Minima
  15. 15The points at which the tangent passes through the origin for the curve are2021Tangent Normal
  16. 16If the radius of a sphere is measured as with an error of , then find the approximating error in calculating its volume.2021Rate Measure Error and Approximation
  17. 17is2021Monotonicity
  18. 18If the tangent at on meets the curve again at , then is2021Tangent Normal
  19. 19Consider the function then is2020Maxima Minima
  20. 20Let and then the greatest of is2020Maxima Minima
  21. 21The equation of the tangent to the curve at the point where it crosses the -axis is2020Tangent Normal
  22. 22Suppose that and for all values of Then, the largest value which can attain is2020Mean Value Theorem
  23. 23If f and g are differentiable function in 0 , 1 satisfying f 0 = 2 = g 1 , g 0 = 0 and f 1 = 6 , then for some c 0 , 12019Maxima Minima
  24. 24The least value of the function f ( x ) = 0 x 3 sin x + 4 cos x d x in the interval 5 4 , 4 3 is2019Maxima Minima
  25. 25The difference of maximum and minimum values of f ( x ) = x 2 e - x is2019Maxima Minima
  26. 26The distance between the origin and the normal to curve y = e 2 x + x 2 at x = 0 is2019Tangent Normal
  27. 27An inverted conical flask is being filled with water at the rate of 3 cm 3 sec - 1 . The height of the flask is 10 cm and the radius of the 2018Maxima Minima
  28. 28For which interval the given function f x = - 2 x 3 - 9 x 2 - 12 x + 1 is decreasing?2018Monotonicity
  29. 29Let f x = - 2 x 3 + 21 x 2 - 60 x + 41 , then2017Monotonicity
  30. 30Rolle s theorem is not applicable for the function f ( x ) = | x | in the interval [ - 1 , 1 ] because2017Mean Value Theorem
  31. 31If the curve y = a x and y = b x intersect at angle , then tan is equal to2017Tangent Normal
  32. 32The maximum value of f ( x ) = x + sin 2 x , x [ 0 , 2 ] is2017Monotonicity
  33. 33Line joining the points ( 0 , 3 ) and ( 5 , - 2 ) is a tangent to the curve y = a x 1 + x , then2017Tangent Normal
  34. 34The shortest distance between the parabolas y 2 = 4 x and y 2 = 2 x - 6 is2017Maxima Minima
  35. 35The set of all values of a for which the function does not possess critical points is2016Maxima Minima
  36. 36What is the -coordinate of the point on the curve where the tangent is parallel to -axis?2016Tangent Normal
  37. 37Consider the following statements in respect of the function I. is increasing in [-1,1] II. has no root in (-1,1) . Which of the statements 2016Monotonicity
  38. 38At an extreme point of a function the tangent to the curve is2016Maxima Minima
  39. 39The curve has minimum value equal to2016Maxima Minima
  40. 40The line which is parallel to X-axis and crosses the curve at an angle of , is2015Tangent Normal
  41. 41The number of real roots of the equation e is2015Mean Value Theorem
  42. 42Tangents are drawn from the origin to the curve Their points of contact lie on2015Tangent Normal
  43. 43The slope of the tangent to the curve cos is minimum at , then the value of is2015Tangent Normal
  44. 44The function has a local minimum at2015Maxima Minima
  45. 45If \(0<x< { }{2}\), then2015Maxima Minima
  46. 46Let be a polynomial of degree three satisfying and is a stationary point of If does not have an extremum at , then the value of is2015Maxima Minima
  47. 47The interval in which the function increases less rapidly than the function is2014Monotonicity
  48. 48The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and costs ' 48 per hour at 16 m2014Maxima Minima
  49. 49The equation of all lines having slope 2 which are tangent to the curve is2013Tangent Normal
  50. 50The function is increasing in the set2013Monotonicity

Frequently Asked Questions

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

This chapter includes 67 questions compiled from BITSAT papers spanning 2009 to 2024.

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

These are BITSAT 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 BITSAT Mathematics?

Application of Derivatives has appeared in 16 of the 16 years of BITSAT papers covered here, with 67 questions across 19 papers - about 4 per paper it appears in.

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

Of the 67 questions analysed for this chapter, 37% are easy, 52% moderate and 10% tough. 2024 had the most, with 7 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 - 22 questions (33%)
  • Tangent Normal - 18 questions (27%)
  • Monotonicity - 17 questions (25%)
  • Maxima Minima has produced the most tough questions (2).
6.Is Application of Derivatives's weightage in BITSAT going up or down?

Across all 19 papers analysed, Application of Derivatives has averaged about 3.5 questions per paper. In the last three years (2022–2024), that average has fallen, at about 2.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.