NCERT Class 12 Mathematics Chapter 12: Linear Programming MCQs & PYQs

In NCERT Class 12 Mathematics Chapter 12, titled Linear Programming, students explore the method of formulating and solving linear programming problems (LPP). This chapter discusses objective functions, constraints, and feasible regions, enabling students to solve optimization problems effectively. Applications of linear programming are found in various fields such as economics, business, and engineering, where optimal resource allocation is essential.

This article serves as a complete guide for preparing Class 12 Mathematics Chapter 12. It includes MCQs, subjective questions, and solutions, along with downloadable PDFs of CBSE and CUET questions.

NCERT Class 12 Mathematics Chapters
Chapter 1: Relations and Functions	Chapter 2: Inverse Trigonometric Functions
Chapter 3: Matrices	Chapter 4: Determinants
Chapter 5: Continuity and Differentiability	Chapter 6: Application of Derivatives
Chapter 7: Integrals	Chapter 8: Application of Integrals
Chapter 9: Differential Equations	Chapter 10: Vector Algebra
Chapter 11: Three Dimensional Geometry	Chapter 13: Probability

Class 12 Mathematics Chapter 12 MCQs

This section includes CUET and CBSE MCQs, along with curated questions by subject experts. Below are 5 sample MCQs for Class 12 Mathematics Chapter 12: Linear Programming. For the full set of 50 MCQs, download the PDF using the link below.

1.	The graph of the inequality 2x + 3y > 6 is (a) half plane that contains the origin. (b) half plane that neither contains the origin nor the points of the line 2x + 3y = 6. (c) whole XOY – plane excluding the points on the line 2x + 3y = 6. (d) entire XOY plane.
2.	The corner points of the feasible region in the graphical representation of a linear programming problem are (2, 72), (15, 20) and (40, 15). If z = 18x + 9y be the objective function, then : (a) z is maximum at (2, 72), minimum at (15, 20) (b) z is maximum at (15, 20), minimum at (40, 15) (c) z is maximum at (40, 15), minimum at (15, 20) (d) z is maximum at (40, 15), minimum at (2, 72)
3.	The number of corner points of the feasible region determined by the constraints x - y ≥ 0, 2y ≤ x + 2, x ≥ 0, y ≥ 0 is : (a) 2 (b) 3 (c) 4 (d) 5
4.	The objective function 𝑍 = 𝑎𝑥 + 𝑏𝑦 of an LPP has maximum value 42 at (4, 6) and minimum value 19 at (3, 2). Which of the following is true? (a) 𝑎 = 9, 𝑏 = 1 (b) 𝑎 = 5, 𝑏 = 2 (c) 𝑎 = 3, 𝑏 = 5 (d) 𝑎 = 5, 𝑏 = 3
5.	The corner points of the feasible region of a linear programming problem are (0, 4),(8, 0) and <. If 𝑍 = 30𝑥 + 24𝑦 is the objective function, then (maximum value of 𝑍 − minimum value of 𝑍) is equal to: (a) 40 (b) 96 (c) 120 (d) 144

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Class 12 Mathematics Chapter 12 Subjective Questions Without Solutions

This section includes previous years' CBSE subjective questions (2 marks and above) and expert-curated questions. Below are 5 sample subjective questions for Class 12 Mathematics Chapter 12: Linear Programming. For the complete set of subjective questions, download the PDF using the link below.

1.	Solve graphically the following linear programming problem : Maximize z = 6x + 3y, subject to the constraints 4x + y ≥ 80, 3x + 2y ≤ 150, x + 5y ≥ 115, x ≥ 0, y ≥ 0. (CBSE 2023, 3M)
2.	Maximize P = 100x + 5y subject to the constraints x + y ≤ 300, 3x + y ≤ 600, y ≤ x + 200, x, y ≥ 0. (CBSE 2023, 3M)
3.	Maximize z = 600x + 400y subject to the constraints : x + 2y ≤ 12, 2x + y ≤ 12, x + 1·25y ≥ 5, x, y ≥ 0 (CBSE 2023, 3M)
4.	Minimize : Z = 5x + 10y subject to constraints : x + 2y ≤ 120, x + y ≥ 60, x - 2y ≥ 0, x ≥ 0, y ≥ 0 (CBSE 2023, 3M)
5.	Maximize: 𝑍 = 𝑥 + 2𝑦 subject to constraints: 𝑥 + 2𝑦 ≥ 100, 2𝑥 − 𝑦 ≤ 0, 2𝑥 + 𝑦 ≤ 200, 𝑥 ≥ 0, 𝑦 ≥ 0 (CBSE 2023, 3M)

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Class 12 Mathematics Chapter 12 Sub Topics

Chapter Name	Sub Topic Name
Linear Programming	12.1 Introduction to Linear Programming
	12.2 Linear Inequalities
	12.3 Graphical Representation of LPP
	12.4 Feasible and Infeasible Regions
	12.5 Optimal Solutions
	12.6 Applications of Linear Programming

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Review of NCERT Class 12 Mathematics Chapter 12

NCERT Class 12 Mathematics Chapter 12, Linear Programming, introduces students to optimization techniques that are essential for decision-making in real-world problems. This chapter covers key concepts such as constraints, feasible regions, and optimization of objective functions, making it a fundamental topic in mathematics. Mastery of this chapter is crucial for students preparing for CBSE, CUET, and other competitive exams.

By solving the provided MCQs and subjective questions, students can gain confidence and enhance their problem-solving abilities in linear programming.

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