NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise 6 AOD – Application of Derivatives in Hindi Medium as well as English Medium Based on latest CBSE Curriculum 2019-2020 for CBSE and other Boards. Download NCERT Solutions and CBSE Solutions Apps updated for new session.

Class 12: | Maths |

Application of Derivatives | Miscellaneous Exercise 6 |

Table of Contents

## NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise 6

### Class 12 Maths Chapter 6 Miscellaneous Exercise Solutions in English

NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise 6 AOD – Application of Derivatives in English Medium free to download or view online. Click here to go back to Class 12 Maths Chapter 6 all exercises or go for Hindi Medium Solutions.

#### Class 12 Maths Chapter 6 Miscellaneous Exercise Solutions in Hindi

NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise 6 AOD – Application of Derivatives in Hindi Medium free to use online. Click here to go back to Class 12 Maths Chapter 6 all exercises or go for English Medium solutions.

Go to Hindi Medium or English Medium solutions

##### Questions From Board Papers

- The volume of a cube is increasing at a constant rate. Prove that the increase in its surface area varies inversely as the length of an edge of the cube.
- The sides of an equilateral triangle are increasing at the rate of 2cm/s. Find the rate at which the area increases, when the side is 10cm.
- A conical vessel whose height is 10 meters and the radius of whose base is half that of the height is being filled with a liquid at a uniform rate of 1.5 m³/min. Find the rate at which the level of the water in the vessel is rising when it is 3m below the top of the vessel.
- If the areas of a circle increases at a uniform rate, then prove that the perimeter various inversely as the radius.
- Find a point on the parabola f(x) = (x − 3)² where the tangent is parallel to the chord joining the points (3,0) and (4,1).

###### Important Questions

- Show that the tangents to the curve y = 2x³ − 3 at the point where x = 2 and x = -2 are parallel.
- If the radius of a circle increases from 5 cm to 5.1 cm, find the increase in area.
- The sum of the surface areas of cuboids with sides x, 2x and x/3 and a sphere is given to be constant. Prove that the sum of their volumes is minimum if x = 3 radius of the sphere. Also find the minimum value of the sum of their volumes.
- Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.
- Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius r is 2r/√3.