NCERT MCQ CLASS-12 CHAPTER-12 | MATH NCERT MCQ | LINEAR PROGRAMMING | EDUGROWN

In This Post we are  providing Chapter-12 Linear Programming NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON LINEAR PROGRAMMING

Question 1.
Feasible region in the set of points which satisfy
(a) The objective functions
(b) Some the given constraints
(c) All of the given constraints
(d) None of these

Answer: (c) All of the given constraints

Question 2.
Of all the points of the feasible region for maximum or minimum of objective function the points
(a) Inside the feasible region
(b) At the boundary line of the feasible region
(c) Vertex point of the boundary of the feasible region
(d) None of these

Answer: (c) Vertex point of the boundary of the feasible region

Question 3.
Objective function of a linear programming problem is
(a) a constraint
(b) function to be optimized
(c) A relation between the variables
(d) None of these

Answer: (b) function to be optimized

Question 4.
A set of values of decision variables which satisfies the linear constraints and n-negativity conditions of a L.P.P. is called its
(a) Unbounded solution
(b) Optimum solution
(c) Feasible solution
(d) None of these

Answer: (c) Feasible solution

Question 5.
The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x ≥ 0, y ≥ 0 is
(a) 300
(b) 600
(c) 400
(d) 800

Answer: (b) 600

Question 6.
The maximum value of Z = 4x + 2y subject to the constraints 2x + 3y ≤ 18, x + y ≥ 10, x, y ≤ 0 is
(a) 36
(b) 40
(c) 30
(d) None of these

Answer: (d) None of these

Question 7.
In equation 3x – y ≥ 3 and 4x – 4y > 4
(a) Have solution for positive x and y
(b) Have no solution for positive x and y
(c) Have solution for all x
(d) Have solution for all y

Answer: (a) Have solution for positive x and y

Question 8.
The maximum value of Z = 3x + 4y subjected to constraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is
(a) 120
(b) 140
(c) 100
(d) 160

Answer: (b) 140

Question 9.
Maximize Z = 11 x + 8y subject to x ≤ 4, y ≤ 6, x + y ≤ 6, x ≥ 0, y ≥ 0.
(a) 44 at (4, 2)
(b) 60 at (4, 2)
(c) 62 at (4, 0)
(d) 48 at (4, 2)

Answer: (b) 60 at (4, 2)

Question 10.
Maximize Z = 3x + 5y, subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0
(a) 20 at (1, 0)
(b) 30 at (0, 6)
(c) 37 at (4, 5)
(d) 33 at (6, 3)

Answer: (c) 37 at (4, 5)

Question 11.
Maximize Z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0
(a) 16 at (4, 0)
(b) 24 at (0, 4)
(c) 24 at (6, 0)
(d) 36 at (0, 6)

Answer: (d) 36 at (0, 6)

Question 12.
Maximize Z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0
(a) 59 at (92, 52)
(b) 42 at (6, 0)
(c) 49 at (7, 0)
(d) 57.2 at (0, 5.2)

Answer: (a) 59 at (92, 52)

Question 13.
Maximize Z = 6x + 4y, subject to x ≤ 2, x + y ≤ 3, -2x + y ≤ 1, x ≥ 0, y ≥ 0
(a) 12 at (2, 0)
(b) 1403 at (23, 13)
(c) 16 at (2, 1)
(d) 4 at (0, 1)

Answer: (c) 16 at (2, 1)

Question 14.
Maximize Z = 10 x₁ + 25 x₂, subject to 0 ≤ x₁ ≤ 3, 0 ≤ x₂ ≤ 3, x₁ + x₂ ≤ 5
(a) 80 at (3, 2)
(b) 75 at (0, 3)
(c) 30 at (3, 0)
(d) 95 at (2, 3)

Answer: (d) 95 at (2, 3)

Question 15.
Z = 20x₁ + 20₂, subject to x₁ ≥ 0, x₂ ≥ 0, x₁ + 2x₂ ≥ 8, 3x₁ + 2x₂ ≥ 15, 5x₁ + 2x₂ ≥ 20. The minimum value of Z occurs at
(a) (8, 0)
(b) (52, 154)
(c) (72, 94)
(d) (0, 10)

Answer: (c) (72, 94)

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