# NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4

NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4 AOD – Application of Derivatives (Approximation) in Hindi Medium as well as English Medium for all students using latest Books and NCERT Solutions for 2020-2021.

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## NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4

Class: | 12 |

Subject: | Maths |

Chapter 6: | Exercise 6.4 |

### 12th Maths Exercise 6.4 Solutions

NCERT Solutions for Class 12 Maths Exercise 6.4 AOD – Application of Derivatives in English Medium and Hindi Medium free to download or view online updated for new session based on latest NCERT Books 2020-21. Ask your doubts related to NIOS and CBSE through Discussion Forum and reply to the questions asked by your friends.

### Exercise 6.4 Solutions in Hindi & English

#### Class 12 Maths Chapter 6 Exercise 6.4 Solutions in Videos

#### QUESTIONS FROM BOARD PAPERS

1. In a competition, a brave child tries to inflate a huge spherical balloon bearing slogans against child labour at the rate of 900 cm3 of gas per second. Find the rate at which the radius of the balloon is increasing, when its radius is 15 cm. Why is child labour not good for society?

2. A kite is moving horizontally at a height of 151.5 meters. If the speed of the kite is 10m/sec, how fast is the string being let out when the kite is 250 m away from the boy who is flying the kite? The height of the boy is 1.5 m.

3. A man 2m tall, walk at a uniform speed of 6 km/h away from a lamp post 6m high. Find the rate at which the length of his shadow increases.

4. x and y are the sides of two squares such that y = x – x² . Find the rate of change of area of the second square w.r.t. the area of the first square.

5. Show that f(x) = x³ – 6x² + 18x + 5 is an increasing function for all x ∈ R. Find its value when the rate of increase of f(x) is least.

##### Important Questions for Practice

1. For the curve y = 5x – 2x³, if x increases at the rate of 2 units/sec. then how fast is the slope of the curve changing when x=3?

2. If the side of a cube be increased by 0.1%, find the corresponding increase in the volume of the cube.

3. The radius of a sphere shrinks from 10 cm. to 9.8 cm. Find the approximately decrease in its volume.

4. Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is 6r√3.

5. Show that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/27 of the volume of the sphere.

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