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Mathematics - Application of Derivatives

Practise 28 KVPY previous year questions on Application of Derivatives, compiled from papers spanning 2010 to 2020. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty KVPY tests.

  1. 1Let R be the set of all real numbers and f ( x ) = sin 10 x cos 8 x + cos 4 x + cos 2 x + 1 for x R . Let S = { R there exits a point c ( 0 2020 (SB/SX)
  2. 2The maximum value of the function f ( x ) = e x + x ln x on the interval 1 x 2 is2020 (SB/SX)
  3. 3Let f ( x ) = sin x + x 3 - 3 x 2 + 4 x - 2 cos x for x ( 0 , 1 ) . Consider the following statements I. f has a zero in 0 , 1 II. f is mono2020 (SB/SX)
  4. 4For [ 0 , ] , let f ( ) = sin ( cos ) and g ( ) = cos ( sin ) . Let a = max 0 f , b = min 0 = f , c = max 0 9 g and d = min 0 g . The correc2020 (SB/SX)
  5. 5Among all the parallelograms whose diagonals are 10 and 4 , the one having maximum area has its perimeter lying in the interval2019 (SB/SX)
  6. 6A rectangle with its sides parallel to the X -axis and Y -axis is inscribed in the region bounded by the curves y = x 2 - 4 and 2 y = 4 - x 2018 (SB/SX)
  7. 7The number of polynomials p : R R satisfying p 0 = 0 , p x x 2 for all x 0 and p ' ' 0 = 1 2 is2018 (SB/SX)
  8. 8A sector is removed from a metallic disc and the remaining region is bent into the shape of a circular conical funnel with volume . The leas19 Nov, 2017 (SB/SX)
  9. 9In an isosceles trapezium, the length of one of the parallel sides, and the leng ths of the non-parallelsides are all equal to 30 . In order05 Nov, 2017 (SA)
  10. 10Let be real numbers such that . Then the smallest possible value of the expression lies in the interval05 Nov, 2017 (SA)
  11. 11Suppose are real numbers such that The maximum possible value of is05 Nov, 2017 (SB/SX)
  12. 12A solid hemisphere is mounted on a solid cylinder, both having equal radii. If the whole solid is to have a fixed surface area and the maxim05 Nov, 2017 (SB/SX)
  13. 13There are two candles of same length and same size. Both of them burn at uniform rate. The first one burns in 5 hours and the second one bur2016 (SA)
  14. 14Ten ants are on the real line. At time , the -th ant starts at the point and travelling at uniform speed, reaches the point at time . The nu2016 (SB/SX)
  15. 15On the real line , we define two functions and as follows: Where denotes the largest integer not exceeding The positive integer for which is2016 (SB/SX)
  16. 16Let be a non-negative differentiable function on such that and for all . Then, on2016 (SB/SX)
  17. 17The range of the polynomial as varies over the interval is2016 (SB/SX)
  18. 18Let where is a real constant. The smallest for which for all is2015 (SB/SX)
  19. 19Let . The number of real roots of is2013 (SB/SX)
  20. 20Let be a natural number and let 'a' be a real number. The number of zeros of in the interval is2012 (SB/SX)
  21. 21Let , then-2012 (SB/SX)
  22. 22A piece of paper in the shape of a sector of a circle (see Fig. 1) is rolled up to form a right-circular cone (see Fig. 2). The value of the2011 (SA)
  23. 23The diameter of one of the bases of a truncated cone is . If the diameter of this base is increased by such that it still remains a truncate2011 (SA)
  24. 24Let , where are real numbers. If has a local minimum at and a local maximum at and , then equals-2011 (SB/SX)
  25. 25The figure shown below is the graph of the derivative of some function . Then-2010 (SB/SX)
  26. 26Let be a differentiable function such that and a) for some . Then the minimum number of roots of in the interval is-2010 (SB/SX)
  27. 27Let be the volume of a given right circular cone with as the centre of the base and as its apex. Let be the maximum volume of the right circ2010 (SB/SX)
  28. 28The following figure shows the graph of a differentiable function on the interval (not containing 0 ). Let which of the following is a possi2010 (SB/SX)

Frequently Asked Questions

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

This chapter includes 28 questions compiled from KVPY papers spanning 2010 to 2020.

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

These are KVPY 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 KVPY Mathematics?

Application of Derivatives has appeared in 10 of the 11 years of KVPY papers covered here, with 28 questions across 14 papers - about 2 per paper it appears in.