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CBSE - Class 12 > Mathematics > Application of Derivatives Worksheets

Free CBSE - Class 12 Mathematics - Application of Derivatives worksheets

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1.
For all real values of $x$, the minimum value of $\frac{1-x+x^2}{1+x+x^2}$ is
1. 0 2. 1 3. 3 4. $\frac{1}{3}$
2.
The maximum value of $[x(x-1)+1]^{\frac{1}{3}}$, $0 \le x \le 1$ is
1. $(\frac{1}{3})^{\frac{1}{3}}$ 2. $\frac{1}{2}$ 3. 1 4. 0
3.
Find two positive numbers whose sum is $16$ and the sum of whose cubes is minimum.
4.
A square piece of tin of side $18$ cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.
5.
A rectangular sheet of tin $45$ cm by $24$ cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?
6.
Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.
7.
Of all the closed cylindrical cans (right circular), of a given volume of $100$ cubic centimetres, find the dimensions of the can which has the minimum surface area?
8.
Prove that the volume of the largest cone that can be inscribed in a sphere of radius $R$ is $\frac{8}{27}$ of the volume of the sphere.
9.
Show that the right circular cone of least curved surface and given volume has an altitude equal to $\sqrt{2}$ time the radius of the base.
10.
Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is $\tan^{-1} \sqrt{2}$.
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Chapters in CBSE - Class 12 Mathematics

Relations and Functions Worksheet Inverse Trigonometric Functions Worksheet Matrices Worksheet Determinants Worksheet Continuity and Differentiability Worksheet Integrals Worksheet Application of Integrals Worksheet Differential Equations Worksheet Vector Algebra Worksheet Three Dimensional Geometry Worksheet Linear Programming Worksheet Probability Worksheet

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Top Concept Videos in Mathematics Application of Derivatives

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