Miscellaneous ch 6 class 12

NCERT Solutions for Class 12 Maths Chapter-6 Application of Derivatives Miscellaneous Examples Free PDF download of NCERT Solutions for Class 12 Maths Chapter 6 miscellaneous prepared by expert Mathematics teacher at Mathongo.com as per CBSE (NCERT) books guidelines. Download our Class 12 Maths Chapter 6 Application of Derivatives miscellaneous Questions with Solutions to help you to revise complete Syllabus and Score More marks in your exams. FREE PDF • • • • • • • • • • • • • • • • • • • • • • • •

Table of Contents • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • NCERT Solutions class 12 Maths Miscellaneous Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free. Download NCERT Solutions for Class 12 Maths Application of Derivatives 1. Using differentials, find the approximate value of each of the following: (a) (b) Ans. (a) Let ……….(i) = ……….(ii) Changing to and to in eq. (i), we have ……….(iii) Here and From eq. (iii), 0.677 (b) Let ……….(i) = ……….(ii) Changing to and to in eq. (i), we have …….(iii) Here and From eq. (iii), 0.497 2. Show that the function given by has maximum value at Ans. Here ……….(i) ……..(ii) And = ……….(iii) Now From eq. (iii), = = 0 (i) is increasing if , i.e., from eq. (i), lies in I and IV quadrants, i.e., is increasing for and and (ii) is decreasing if , i.e., from eq. (i), lies in II and III quadrants, i.e., is decreasing for 7. Find the intervals in which the function given by is (i) increasing (ii) decreasing. Ans. (i) Given: = = = ……….(i) Now = 0 = 0 Here, is positive for all real or [Turning points] Therefore, or divide th...

NCERT Solutions for Class 12 Maths Miscellaneous Exercise Chapter 6 Application of Derivatives NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives Miscellaneous Exercise – Free PDF Download NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives contain solutions for all Miscellaneous Exercise questions. The aim of NCERT solutions is to give students the advantage of preparing themselves for the CBSE board exams. Students can download the Access Answers to Maths NCERT Class 12 Chapter 6 Application of Derivatives Miscellaneous Exercise Page number 242 Access other exercise solutions of Class 12 Maths Chapter 6 Application of Derivatives NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives Miscellaneous Exercise • Introduction • Rate of Change of Quantities • Increasing and Decreasing Functions • Tangents and Normals • Approximations • Maxima and Minima • Maximum and Minimum Values of a Function in a Closed Interval Also, explore –Â

Tiwari Academy / NCERT Solutions / NCERT Solutions for Class 12 / NCERT Solutions for Class 12 Maths / NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions / NCERT Solutions Class 12 Maths Chapter 1 Miscellaneous Exercise NCERT Solutions Class 12 Maths Chapter 1 Miscellaneous Exercise In Class 12 Maths Chapter 1 Miscellaneous Exercise, the basic questions are based on Exercise 1.1 or Exercise 1.2. Some question which are based on to find the inverse of function are based on Exercise 1.3. Questions based on Binary Operation are also given which we have learnt in Exercise 1.4. It is just a good practice of all the exercises. Universal relation is the relation R in X given by R = X × X. Empty relation is the relation R in X given by R = φ ⊂ X × X. The miscellaneous exercise is one of the most important exercise for the board exams. Apart from this, student must do the examples given just before the miscellaneous exercise. These are frequently asked in board exam papers. Provide your feedback to help us in improving the contents. Download Offline Apps following the current CBSE Syllabus for all boards who are using NCERT Books. Join the Miscellaneous exercise of chapter 1 (class 12th Maths) has 11 examples (examples 41 to 51) and 19 questions. All questions and examples of this exercise are nice, interesting and logical. All problems of this exercise are important for exams, but the most important problems are examples 41, 42, 43, 45, 46, 47, 48, 51 and qu...

Students can get the NCERT solutions for Class 12 Maths chapter 6 miscellaneous exercise on this page. The Class 12 Maths chapter 6 miscellaneous exercise solutions are designed to make the students understand the applications of concepts studies in the NCERT book. Class 12 Maths chapter 6 miscellaneous solutions covers all the topics discussed in the previous exercises. Miscellaneous exercise chapter 6 Class 12 presents questions to practice the complete chapter. One should visit the Table of contents After completing all the topics of NCERT syllabus Class 12 Maths chapter 6 and solved and unsolved questions of all other exercises the miscellaneous exercise can be attempted. The miscellaneous exercise combines questions from the complete chapter and the level of questions compared to exercises will be a bit higher. The following exercises are also present in the chapter. • • • • • Question:4 which passes through the point (1, 2). Answer: Given the equation of the curve We know that the slope of the tangent at a point on the given curve is given by We know that At point (a,b) Now, the equation of normal with point (a,b) and It is given that it also passes through the point (1,2) Therefore, -(i) It also satisfies equation -(ii) By comparing equation (i) and (ii) Now, equation of normal with point (2,1) and slope = -1 Hence, equation of normal is x + y - 3 = 0 Question:5 . to the curve is at a constant distance from the origin. Answer: We know that the slope of tangent at an...

Tiwari Academy / NCERT Solutions / NCERT Solutions for Class 12 / NCERT Solutions for Class 12 Maths / NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry / NCERT Solutions Class 12 Maths Chapter 11 Miscellaneous Exercise NCERT Solutions Class 12 Maths Chapter 11 Miscellaneous Exercise A plane is determined uniquely if any one of the following is known: • The normal to the plane and its distance from the origin is given, i.e., equation of a plane in normal form. • It passes through a point and is perpendicular to a given direction. • It passes through three given non collinear points. • 1. If d is the distance from the origin and l, m, n are the normal cosines of the plane direction through the origin, the foot of the perpendicular is (ld, md, nd). • 2. Do you know why was it necessary to say that the three points had to be non collinear? If the three points were on the same line, then there will be many planes that will contain them. • 3. The angle between two planes is defined as the angle between their normal. • 4. The planes are perpendicular to each other if n1.n2 = 0 and parallel if n1 is parallel to n2. • 5. The angle between a line and a plane is the complement of the angle between the line and normal to the plane.

NCERT Solutions for Class 11 Maths Chapter 6 - Linear Inequalities Miscellaneous Exercise * According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 5. Chapter 6 Linear Inequalities of Class 11 Maths is categorised under the CBSE Syllabus for 2023-24. The last exercise of the chapter, the miscellaneous exercise, contains 14 questions that cover the topics from the entire chapter. The Miscellaneous Exercise of • Introduction to Linear Inequalities • Inequalities • Algebraic Solutions of Linear Inequalities in One Variable and Their Graphical Representation The latest CBSE guidelines are followed while solving the questions in the textbook, and the students can enhance their confidence by solving these questions again and again. Hence, students who aim to get a high score in the Maths board examination should practise solving the Download PDF carouselExampleControls111 Previous Next  Solutions for Class 11 Maths Chapter 6 – Miscellaneous Exercise Solve the inequalities in Exercises 1 to 6. 1. 2 ≤ 3x – 4 ≤ 5 Solution: According to the question, The inequality given is 2 ≤ 3x – 4 ≤ 5 ⇒ 2 ≤ 3x – 4 ≤ 5 ⇒ 2 + 4 ≤ 3x – 4 + 4 ≤ 5 + 4 ⇒ 6 ≤ 3x ≤ 9 ⇒ 6/3 ≤ 3x/3 ≤ 9/3 ⇒ 2 ≤ x ≤ 3 Hence, all real numbers x greater than or equal to 2 but less than or equal to 3 are solutions of given equality. x ∈ [2, 3] 2. 6 ≤ –3 (2x – 4) -4 [multiplying the inequality with -1 changes the inequality sign.] ⇒ ...