NCERT Solutions for Complex Numbers and Quadratic Equations Exercise 5.3 Class 11 Maths

September 13, 202239 Insightful Publications

**NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming: **Chapter 12 of CBSE Class 12 Maths covers the important concepts of Linear Programming. Students must thoroughly understand Linear Programming concepts to score good marks in the board exams. Being thorough with the in-text questions is one of the first steps. Hence, Embibe has provided free NCERT Maths Class 12 Solutions for Chapter 12 for better preparation.

These solutions are designed and prepared by experts in Mathematics at Embibe. Embibe offers at least 500 practice questions from over 20 books on its platform to help students achieve their desired results. These practice questions help students score good marks in board and competitive exams like JEE, NEET, and others. Adding to that, Embibe also explains 27 concepts, including different types of linear programming problems and mathematical formulation of a linear programming problem etc. Visit Embibe to learn more.

In earlier grades, students might have studied systems of linear equations and their applications. Hence, it is expected that students will be able to do sums from linear equations independently. Moreover, the 12th CBSE Maths book and the in-text exercises are very important for the students who want to appear for the board exams and competitive exams in the future.

To help students with their exam preparations, Embibe provides fun learning 3D videos on its platform that engage students with their studies. Embibe broadens students’ minds and helps them learn complex concepts from a different point of view. The topics and sub-topics included in the Linear Programming chapter are as follows:

Sr. No | Topics |
---|---|

1 | Linear Programming Problem and its Mathematical Formulation |

2 | Different Types of Linear Programming Problems |

Below are details related to the NCERT Solutions for Class 12 Maths Chapter 12. Students can check the list of solutions to all the topics in chapter 12 by going through the given exercises.

Below we have provided the crucial points that students must remember about the chapter to score well and achieve great results:

- Linear programming Class 12 Math concepts assist in determining the maximisation or minimisation of various quantities from a general class of problems.
- This is known as an optimisation problem. The linear programming for Class 12 concepts include determining a maximum profit, minimum cost, or minimum use of resources, among other things.
- A linear objective function is a linear function of the form Z = ax + by, where a and b are constants, that must be minimised or maximised.
- An optimisation problem is one in which the goal is to maximise or minimise a linear function (say, of two variables x and y) under certain constraints defined by a set of linear inequalities.
- The feasible region (or solution region) for a linear programming problem is the common region determined by all the given constraints, including non-negative constraints (x ≥ 0, y ≥ 0). An infeasible region is any region that is not feasible.
- These points within and on the boundary of the feasible region represent feasible constraints solutions. An infeasible solution is defined as any point outside the feasible region.
- An optimal solution is any point in the feasible region that gives the optimal value (maximum or minimum) of the objective function.

Students can go through the description of each chapter to get an overview of the contents of the chapters:

- 1st Chapter – Relations and Functions
- 2nd Chapter – Inverse Trigonometric Functions
- 3rd Chapter – Matrices
- 4th Chapter – Determinants
- 5th Chapter – Continuity and Differentiability
- 6th Chapter – Application of Derivatives
- 7th Chapter – Integrals
- 8th Chapter – Application of Integrals
- 9th Chapter – Differential Equations
- 10th Chapter – Vector Algebra
- 11th Chapter – Three Dimensional Geometry
- 12th Chapter – Linear Programming
- 13th Chapter – Probability

**Ans**: Embibe provides NCERT Solutions for all the Class 12 Maths chapters on its platform. Visit Embibe now to learn more.

**Ans**: Here is the list of NCERT Solutions for Class 12 Maths Chapter 12:

1. Class 12 Maths Chapter 12 Exercise 12.1: Introduction

2. Class 12 Maths Chapter 12 Exercise 12.2: Linear Programming Problem and its Mathematical Formulation

3. Class 12 Maths Chapter 12 Exercise 12.3: Different Types of Linear Programming Problems

Miscellaneous

**Ans**: Linear programming is used for obtaining the best solution for a problem with given constraints. In linear programming, we formulate our real-life problem into a mathematical model. It involves an objective function, linear inequalities with subject to constraints.

**Ans**: Around 27 concepts for Linear Programming are covered by Embibe for free.

**Ans**: There are over 500 practice questions for Linear Programming on Embibe that will help students score excellent marks. These practice questions are available for free to all the students.

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