NCERT Exemplar Class 12 Maths Chapter 9 Solutions: Differential Equations
NCERT Exemplar Class 12 Maths Solutions Chapter 9 ‘Differential Equations’ are designed to give you in-depth knowledge of this topic. It is one of the crucial topics from the perspective of competitive exams like JEE Mains and JEE Advance. Moreover, it has good weightage in CBSE NCERT Exemplar Class 12 Maths board exams.
In this chapter, there are 77 exemplar problems divided into various exercises. These questions are framed as short-answer type, long-answer type, multiple-choice questions (MCQs), true-false questions, and fill in blanks type questions. These questions are set up so that you can assemble essential ideas required to tackle similar problems in the exams.
Instasolv’s NCERT exemplar problems with solutions are made after complete research of the latest CBSE Class 12 Maths syllabus for differential equations. You will encounter topics like the order of differential equations, degree of differential equations, variable separable method, homogeneous differential equations and first-order linear differential equations.
Important Topics for NCERT Exemplar Class 12 Maths Solutions Chapter 9 – Differential Equations
In NCERT Exemplar Class 12 Maths problems and solutions for chapter 9, you need to understand the basic concepts of the differential equation. You will study the solutions of a differential equation in standard form, the formulation of differential equations, and its various applications. There is also a great emphasis on some of the essential methods to solve a first-order differential equation as well.
There are essential discussions on the degree of a differential equation and which form will represent which family of the curve. It will help build the conceptual knowledge of this chapter. There are other important topics, such as first-degree differential equations and homogeneous differential equations. Towards the end, linear differential equations and differential equations with variables separable are analyzed in detail.
Here are some important points for NCERT Exemplar Problems and Solutions for Class 12 Maths Chapter 9 ‘Differential Equations’:
- Differential Equation: It is an equation which involves a derivative of the dependent variable with respect to the independent variable
- Ordinary differential equation: A differential equation which involves derivatives of the dependent variable with respect to only one independent variable
- Partial differential equation: A differential equation involving derivatives with respect to more than one independent variable.
- Linear differential equation: When the variable in a differential equation has the power of one.
- Non-linear differential equation: When the variable in a differential equation has powered more than one.
- Order: For a differential equation, the order of the highest order derivative, which is occurring in the differential equation, is commonly known as its order.
- Degree: It is defined if the differential equation is a polynomial equation in its derivatives. It is the highest power of the highest order derivative in it.
- General Solution: The solution which contains the same number of arbitrary constants as the order of the differential equation
- Particular Solution: The solution which is free from arbitrary constants is called a particular solution.
Exercise Discussion of NCERT Exemplar Class 12 Maths Solutions Chapter 9 – Differential Equations
- The first 24 exemplar problems are short answer types. They test your necessary skills and formula applications on topics like solving differential equations, finding the general solution.
- The next 9 exemplar questions from 25-33 are long answer types, which are based mostly on numerical problems on general solutions of differential equations and equations of a curve.
- MCQs are given the main emphasis in this exercise due to the high weightage in competitive exams. From questions 34-75 are MCQs based order and degree of differential equations, solutions of differential equations, integrating factor, etc.
- Question 76 has 11 sub-parts to it which are fill-in the blanks problems and question 77 includes 10 sub-parts of true-false questions based on all the topics of the chapter.
Why Use NCERT Exemplar Class 12 Maths Solutions Chapter 9 by Instasolv?
- NCERT Exemplar Class 12 Maths Solutions for Chapter 9 is a very authentic source of learning. Class 12 is always pressure but our Exemplar problems with solutions will help you a lot.
- We have provided all the solved exemplar problems for chapter 9 online without any cost. It is always suggested by study experts to follow these solutions stepwise to get a clear understanding of the concepts.