Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 12 Linear Programming with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers during preparation and score maximum marks in the exam. Students can download the Linear Programming Class 12 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 12 Maths Chapter 12 Linear Programming Objective Questions.

## Linear Programming Class 12 MCQs Questions with Answers

Students are advised to solve the Linear Programming Multiple Choice Questions of Class 12 Maths to know different concepts. Practicing the MCQ Questions on Linear Programming Class 12 with answers will boost your confidence thereby helping you score well in the exam.

Explore numerous MCQ Questions of Linear Programming Class 12 with answers provided with detailed solutions by looking below.

Question 1.

The point which does not lie in the half plane 2x + 3y -12 < 0 is

(a) (1, 2)

(b) (2, 1)

(c) (2, 3)

(d) (-3, 2).

## Answer

Answer: (c) (2, 3)

Hint:

Putting (2, 3) in 2x + 3y – 12.

Which becomes:

2(2)+ 3(3) – 12 = 4 + 9 – 12 = 1 > 0 and not ≤ 0.

Question 2.

The corner points of the feasible region determined by the following system of linear inequalities:

2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5).

Let Z = px + qy, where p, q > 0. Conditions on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is

(a) p = 3q

(b) p = 2q

(c) p = q

(d) q = 3p.

## Answer

Answer: (d) q = 3p.

Question 3.

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is

(a) p = q

(b) p = 2q

(c) q = 2p

(d) q = 3p.

## Answer

Answer: (d) q = 3p.

Question 4.

The feasible solution for a LPP is shown in the following figure. Let Z = 3x – 4y be the objective function.

Minimum of Z occurs at:

(a) (0, 0)

(b) (0, 8)

(c) (5, 0)

(d) (4, 10).

## Answer

Answer: (b) (0, 8)

Question 5.

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q> 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is Maximum of Z occurs at:

(a) (5, 0)

(b) (6, 5)

(c) (6, 8)

(d) (4, 10).

## Answer

Answer: (a) (5, 0)

Fill in the Blanks

Question 1.

Maximum of Z = x + 2y subject to

x + y ≥ 5, x ≥ 0, y ≥ 0 is …………….. at …………….

## Answer

Answer: 10, (0,5).

Question 2.

Minimum of Z = x + y subject to:

2x + y ≥ 3, x + 2y ≥ 6, x ≥ 0, y ≥ 0 is ………………. at …………….

## Answer

Answer: 3, (0.3).

Question 3.

Maximum and Minimum of Z = 3x + 4 v ≤ 80 subject to 3x + 4v ≤ 80, x + 3y ≤ 30, x ≥ 0, y ≥ 0 are …………….. and …………….

## Answer

Answer: 21600, 0.

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