Ncert Solutions Maths class 12th

Bayes' Theorem results in a formula for conditional Probability which is used to determine the conditional probability of a mutually inclusive event. We have includes usage of this theorem in our Probability solutions in right places. Students can dig deeper into this theorem and learn using its formula through the NCERT Solutions provided by shiksha.

Probability holds good weight in the CBSE Class 2th board exams, Which is why questions based on conditional probability, independent events, and applications of Bayes' Theorem are frequently asked in the board exams. Shiksha's NCERT Solutions for Probability cover all these topics and mentions important formulae and concepts in every question-answer.

The graphical method in Linear Programmin is a visual approach used to find the optimal solution of questions in Linear Programming. We have provided NCERT Solutions for Class 12 Linear Programming and we have discussed graphical solutions of all the questions in the exercises for Class 12 Math Linear Programming. The constraints in linear programming are treated as coordinate point and equations are plotted on a graph as straight lines, and the region that satisfies all of them is known as the feasible region. and area outside it is considered Infeasible regions.

Shiksha's Class 12 Linear Programming, NCERT Solutions provide clear explanation for the concepts of feasible and infeasible regions;

• A feasible region is the common area on a graph that satisfies all the given constraints of a linear programming problem, including non-negativity conditions.
• An infeasible region comprises points that do not satisfy one or more of the problem's constraints. Any point outside the feasible region is considered an infeasible solution.

Students can use NCERT Solutions to understand the concepts for feasible and infeasible reason in the Linear Programming. 

The Class 12 chapter 12 Linear Programming carries a weightage of 5 to 6 marks in the Class 12 CBSE Board Exams. Most of the times one long-answer question and some times 2-3 small answer type questions are asked from this chapter. Our NCERT Solutions will help students get full marks through the practice of enough NCERT questions.

Students can use Shiksa's NCERT Solutions for  Class 12 Linear Programming in PDF format;

• Open Shiksha's NCERT Solutions Link: Chapter 12 Linear Programming Solutions
• Scroll through the Page and click on Download PDF link
• Click on the Download Free PDF
• Save the PDF file in your device offline

There are important topics in Class 12 Linear Programming which are asked in the CBSE 12 Boards. Class 12 Board questions are from important topics such as linear programming problems (LPP), graphical method of solving LPPs, feasible region, bounded/unbounded solutions, and corner point method. Class 12 Linear Programming is asked for around  4-6 mark in CBSE board exams.

Students can use these steps for downloading the PDF for 3D Geometry NCERT Solutions given below;

• Visit the Official Page: Chapter 11 Three dimensional Geometry Solutions
• Access the Solutions and Scroll down to download PDF
• Click on "Download Free PDF"
• Save the PDF in their device

NCERT Solutions for 3D Geometry serves as a mathematical foundation developer for all the students. All competition exam aspirant must use NCERT Textbooks and its solutions for better understanding for fundamental concepts in 3D Geometry. Having a proper understanding of foundation knowledge of chapter is important for competitive exams like JEE and NEET. 

There are various reasons to use Shiksha's NCERT Solutions for 3D Geometry. Students can use 3D Geometry class 12 maths Solutions for various purposes like practice, revision, and making notes. These solutions follow the latest CBSE 2025 syllabus and NCERT textbook pattern. Shiksha Solutions for 3D Geometry are accurate and provide step-by-step explanations of all the questions.