# 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 format Hindi Medium as well as English Medium Based on latest CBSE Curriculum 2021-2022.

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. Miscellaneous Exercise 6 solution in Hindi and English Medium Videos are also given below free to use or download.## NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise

### Class 12 Maths Miscellaneous Exercise 6 Solutions in Hindi & English

Class: 12 | Mathematics |

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 2021-2022. Join the knowledge sharing platform DISCUSSION FORUM to share your view for NIOS board as well as CBSE Board questions already asked.

#### Class 12 Maths Chapter 6 Miscellaneous Exercise 6 Solution in Videos

#### 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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##### Is miscellaneous exercise on chapter 6 of grade 12th Maths interesting to solve?

Most of the students find miscellaneous exercise on chapter 6 of grade 12th Maths challenging compared to other exercises of chapter 6 of class 12th Maths. Questions of this exercise are good, interesting, and require logical thinking. However, the difficulty level of any topic/problem varies from student to student. So, miscellaneous exercise on 6 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.

##### What types of questions are there in miscellaneous exercise on chapter 6 of grade 12th Maths?

Miscellaneous exercise on chapter 6 of grade 12th Maths contains mixed questions based on all concepts (Rate of change of quantities, Increasing and Decreasing functions, Tangents and Normals, Approximations, Maxima and Minima) mentioned in chapter 6 of class 12th Maths. Students can judge their knowledge of chapter 6 of class 12th Maths by doing this exercise.

##### How important the miscellaneous exercise of chapter 6 class 12th Maths in the board exams?

No doubt, the questions can come from miscellaneous exercise on chapter 6 of class 12th Maths in the board exams. This exercise is important from an exam point of view. Students should practice all sums of this exercise for the exams because any question and example can come in the board exams. The problems which have more chance to come in the exams are examples 42, 43, 44, 45, 46, 47, 48, 50 and questions 1, 2, 3, 5, 6, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 23, 24.

##### Is the miscellaneous exercise on chapter 6 of class 12th Maths tricky?

Yes, the miscellaneous exercise on chapter 6 of class 12th Maths is a little lengthy and tricky. The miscellaneous exercise on chapter 6 has 34 problems (10 examples and 24 questions). Students need a maximum of 4-5 days to complete miscellaneous exercise on chapter 6 of class 12th Maths if they give at least 1-2 hours per day to this exercise. This time depends on many factors like student’s working speed, efficiency, capability, etc.