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NCERT Class 12 Mathematics Chapters
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1.
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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.
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2.
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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)
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3.
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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
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4.
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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
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5.
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The corner points of the feasible region of a linear programming problem are (0, 4),(8, 0) and
(a) 40 (b) 96 (c) 120 (d) 144
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1.
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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)
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2.
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Maximize P = 100x + 5y
subject to the constraints
x + y ≤ 300,
3x + y ≤ 600,
y ≤ x + 200,
x, y ≥ 0.
(CBSE 2023, 3M)
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3.
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Maximize z = 600x + 400y
subject to the constraints :
x + 2y ≤ 12,
2x + y ≤ 12,
x + 1·25y ≥ 5,
x, y ≥ 0
(CBSE 2023, 3M)
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4.
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Minimize : Z = 5x + 10y
subject to constraints :
x + 2y ≤ 120,
x + y ≥ 60,
x - 2y ≥ 0,
x ≥ 0, y ≥ 0
(CBSE 2023, 3M)
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5.
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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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Chapter Name
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Sub Topic Name
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Linear Programming
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12.1 Introduction to Linear Programming
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12.2 Linear Inequalities
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12.3 Graphical Representation of LPP
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12.4 Feasible and Infeasible Regions
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12.5 Optimal Solutions
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12.6 Applications of Linear Programming
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