Class 12 Maths CBSE Application of Derivatives Board Questions
Here we provide Class 12 maths important notes,board questions and predicted questions with Answers for chapter Application of Derivatives. These important notes,board questions and predicted questions are based on CBSE board curriculum and correspond to the most recent Class 12 maths syllabus. By practising these Class 12 materials, students will be able to quickly review all of the ideas covered in the chapter and prepare for the Class 12 Board examinations.
Class 12 CBSE Application of Derivatives Board Questions
Application of Derivatives Board Questions
2016
Q1
Show that the equation of normal at any point t on the curve x = 3 cos t - cos3t and y =
3 sin t - sin3t is
4(y cos3t - x sin3t) = 3 sin 4t
solutions
4(y cos3t - x sin3t) = 3 sin 4t
solutions
Q2
Show that the altitude of the right circular cone of maximum volume that can be inscribed in a
sphere of radius r is 4r/3. Also find the maximum volume in terms of volume of the sphere.
OR
Find the intervals in which f(x)= sin3x - cos3x , 0< x < π is strictly increasing or strictly decreasing
solutions
Find the intervals in which f(x)= sin3x - cos3x , 0< x < π is strictly increasing or strictly decreasing
solutions
2017
Q3
The volume of a cube is increasing at the rate of 9 cm3/s . How fast is it surface area
increasing when the length of an edge is 10 cm ?
solutions
solutions
Q4
Show that the function f(x) = x3 - 3x2 + 6x - 100 is increasing on R.
solutions
solutions
Q5
Show that the surface area of a closed cuboid with square base and given volume is minimum when it
is a cube.
solutions
solutions
2018
Q6
Find the equation of tangent to the curve y = √3x - 2 which is parallel to the line 4x - 2y +
5 = 0. Also write the equation of normal to the curve at the point of contact.
solutions
solutions
2019
Q7
Find the angle of intersection of the curves x2 + y2 - 4 and (x
-2)2 + y2 - 4 , at the point in the first quadrant.
OR
Find the intervals in which the function f(x) = -2x3 - 9x2 - 12x + 1 is :
(i) Strictly increasing
(ii) Strictly decreasing
solutions
Find the intervals in which the function f(x) = -2x3 - 9x2 - 12x + 1 is :
(i) Strictly increasing
(ii) Strictly decreasing
solutions
2020
Q8
The equation of the normal to the curve y2 = 8x at the origin is...............
OR
The radius of a circle is increasing at the uniform rate of 3 cm/sec. At instant when the radius of the circle is 2 cm, its area increases at the rate of ..............cm2/s.
solutions
The radius of a circle is increasing at the uniform rate of 3 cm/sec. At instant when the radius of the circle is 2 cm, its area increases at the rate of ..............cm2/s.
solutions
Q9
Show that the height of the right circular cylinder of greatest volume which can be inserted in a
right circular cone of height h and radius r is one-third of the height of the cone, and the
greatest volume of the cylinder is 4/9 times the volume of the cone.
solutions
solutions
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