# NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.5

NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.5 AOD – Application of Derivatives (Maxima and Minima) in Hindi Medium as well as English Medium for all students using latest NCERT Books Solutions for session 2021-22.

Download CBSE Solutions Apps updated as per the latest CBSE Syllabus 2021-22 for CBSE and other Boards. The Video solutions related to 6.5 of 12th Maths in Hindi and English Medium also given below free to access or download.## NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.5

### 12th Maths Exercise 6.5 Solutions in Hindi & English

Class: 12 | Mathematics |

Chapter 6: | Exercise 6.5 |

### 12th Maths Exercise 6.5 Solutions

NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.5 AOD – Application of Derivatives in English Medium Maxima and Minima. NCERT Solutions 2021-2022 are based on latest NCERT Books following the new CBSE Syllabus. Join the Discussion forum to share your knowledge.

#### Class 12 Maths Chapter 6 Exercise 6.5 Solutions in Videos

#### QUESTIONS FROM BOARD PAPERS

1. An inverted cone has a depth of 10 cm and a base of radius 5 cm. Water is poured into it at the rate of 3/2 c.c. per minute. Find the rate at which the level of water in the cone is rising when the depth is 4 cm.

2. A swimming pool is to be drained for cleaning. If L represents the number of litres of water in the pool t seconds after the pool has been plugged off to drain and L = 200(10 − t)². How fast is the water running out at the end of 5 sec. and what is the average rate at which the water flows out during the first 5 seconds?

3. A spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the volume at any instant is proportional to the surface area. Prove that the radius is decreasing at a constant rate.

4. The length of a rectangle is increasing at the rate of 3.5 cm/sec. and its breadth is decreasing at the rate of 3 cm/sec. Find the rate of change of the area of the rectangle when length is 12 cm and breadth is 8 cm.

5. Find the equation of the tangent to the curve y = x² – 2x + 7 which is (1) Parallel to the line 2x − y + 9 = 0 (2) Perpendicular to the line 5y – 15x = 13.

##### Important Questions for Practice

1. Find the equation of the normal at a point on the curve x² = 4y, which passes through the point (1, 2). Also find the equation of the corresponding tangent.

2. Find the point on the curve 9y² = x³ where the normal to the curve makes equal intercepts with the axes.

3. If the sum of length of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is π/3.

4. Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

5. A wire of length 36 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces, so that the combined area of the square and the circle is minimum?

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##### What are the main concepts that students will study in exercise 6.5 of NCERT Book 12th Maths?

In exercise 6.5 of class 12th Maths, students will use the concept of derivatives to calculate the maximum or minimum values of various functions. Students will find the ‘turning points’ of the graph of a function and thus find points at which the graph reaches its highest (or lowest) locally. The knowledge of such points is very important in sketching the graph of a given function. Further, we will find the absolute maximum and absolute minimum of a function that is necessary for the solution of many applied problems.

##### Are there any theorems that students can use to solve questions of exercise 6.5 of class 12th Maths?

Five theorems (Theorems 2, 3, 4, 5, 6) are there that students can use to solve questions of exercise 6.5 of class 12th Maths. These Theorems are easy and interesting. There is no need to do the proofs of these theorems. Students only have to study the statement of the above mentioned theorems. Without these theorems, students cannot solve the questions of exercise 6.5 of grade 12th Maths.

##### How long it takes to prepare exercise 6.5 Class 12th Maths?

Exercise 6.5 of class 12th Maths has 45 problems (16 examples and 29 questions). Students need a maximum of five days to prepare exercise 6.5 (chapter 6) of class 12th Maths if they give 2-3 hours per day to this exercise. This time depends on many factors like student’s working speed, efficiency, capability, etc.

##### Is exercise 6.5 of NCERT Class 12th Maths important for the first term Exam?

Yes, exercise 6.5 of grade 12th Maths is most important from the exam point of view. Every year questions come from exercise 6.5 in the exams. All the questions of this exercise are significant and can come in the exams. But the most important questions of this exercise are examples 28, 30, 32, 33, 35, 37, 38, 40, 41 and questions 1, 2, 5, 7, 9, 11, 12, 14, 15, 18, 19, 20, 22, 23, 24, 25, 26, 28. 4 to 6 marks question can come from this exercise in the board exam.

##### Is exercise 6.5 of 12th Maths difficult to understand?

Exercise 6.5 of class 12th Maths is neither 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 6.5 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.