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 2022-2023. Download Tiwari Academy Solutions Apps updated as per the latest CBSE Curriculum 2022-23 for CBSE and UP Board. Hindi and English Medium Videos related to 12th Maths Ex. 6.4 are given below.

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

### 12th Maths Exercise 6.4 Solutions in Hindi & English

Class: 12 | Mathematics |

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 2022-23. Ask your doubts related to NIOS and CBSE through Discussion Forum and reply to the questions asked by your friends.

#### 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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### What will students learn in exercise 6.4 of 12th standard Maths?

In exercise 6.4 of class 12th Maths, students will study approximations. In this exercise, students will use differentials to approximate values of certain quantities. This exercise is very interesting and logical.

### Is exercise 6.4 of grade 12th Maths simple or tricky to solve and understand?

Exercise 6.4 of class 12th Maths is not very simple and not very hard to solve and understand. It lies in the mid of simple and hard because some examples and questions of this exercise are easy, and some are complex. However, the difficulty level of any topic/problem varies from student to student. So, exercise 6.4 of class 12th Maths is easy, or tough depends on students also. Some students find it complex, some find it simple, and some find it in the middle of easy and difficult.

### Is exercise 6.4 of grade 12th Maths short or lengthy?

Exercise 6.4 of grade 12th Maths is short. Only five examples (examples 21, 22, 23, 24, 25) and nine questions are there in exercise 6.4 of class 12th Maths. Students can easily complete this exercise within three days (approximately) if they give 2 hours per day to this exercise. This time can vary also.

### Which problems of exercise 6.4 of class 12th Maths are similar to each other?

Exercise 6.4 of grade 12th Maths has five examples (examples 21, 22, 23, 24, 25) and nine questions. Examples 21, 22, and question 1 are of the same kind. Example 23, and questions 2, 3, 8 are similar to each other. Example 24, and questions 4, 5, 9 are of the same type. Example 25, and questions 6, 7 are the same.

### Is exercise 6.4 of grade 12th Maths important from the CBSE Exam point of view?

Yes, from the exam point of view, exercise 6.4 of grade 12th math is important. Questions from this exercise can come in the board exams. All questions and examples of this exercise are important. But the most important examples and questions of this exercise are examples 23, 24, 25 and questions 1 (i) (v) (xii) (xiv), 3, 5, 6.