# NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise 6 AOD – Application of Derivatives in PDF form Hindi Medium as well as English Medium Based on latest CBSE Curriculum 2020-2021.

NCERT Solutions are applicable for CBSE and other Boards who are using NCERT Books as course books. Download NCERT Solutions and CBSE Solutions Apps updated for new session.## NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise

Class: | 12 |

Subject: | Maths |

Chapter 6: | Miscellaneous Exercise |

### 12th Maths Miscellaneous Exercise 6 Solutions

NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise 6 AOD – Application of Derivatives in English Medium free to download or view online updated for new academic session 2020-2021. Join the knowledge sharing platform DISCUSSION FORUM to share your view for NIOS board as well as CBSE Board questions already asked.

### Miscellaneous Exercise 6 Solutions in Hindi & English

#### QUESTIONS FROM BOARD PAPERS

1. 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.

2. 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.

3. 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.

4. If the areas of a circle increases at a uniform rate, then prove that the perimeter various inversely as the radius.

5. 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 for Practice

1. Show that the tangents to the curve y = 2x³ − 3 at the point where x = 2 and x = -2 are parallel.

2. If the radius of a circle increases from 5 cm to 5.1 cm, find the increase in area.

3. 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.

4. 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.

5. Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius r is 2r/√3.

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