Mathematics
Multiple Choice Questions (MCQ)
MCQ | Class 12 | Chapter 12
LINEAR PROGRAMMING PROBLEMS
- MCQ Based on the Increasing and Decreasing of Functions.
- MCQ Based on the Equation of Tangent and Slopes.
- MCQ Based on the Maximum and Minimum value of the Functions.
- MCQ Based on Logarithmic and Exponential Functions.
- MCQ Based on the First Derivative Test and Second Derivative Test.
Features
- In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations.
- Solution Hints are also given to some difficult problems.
- Each MCQ contains four options from which one option is correct.
- On the right hand side column of the pdf Answer option is given.
Action Plan
- First of all students should Learn and write all basic points and Formulas related to the Continuity and Differentiability.
- Start solving the NCERT Problems with examples.
- Solve the important assignments on the Applications of Derivatives.
- Then start solving the following MCQ.
MCQ | CHAPTER 12 | CLASS 12
LINEAR PROGRAMMING PROBLEMS
Q 1) Region represented by inequation x ≥ 0, y ≥ 0 is
a) First quadrant
b) Second quadrant
c) Third quadrant
d) Fourth quadrant
Ans: a
Q 2) Which of the following is correct
a) A L.P.P. always has unique solution.
b) Every L.P.P. has an optimal solution.
c) A L.P.P. admits two optimal solutions.
d) If a L.P.P. admits two optimal solutions then it has infinitely many optimal solutions.
a) A L.P.P. always has unique solution.
b) Every L.P.P. has an optimal solution.
c) A L.P.P. admits two optimal solutions.
d) If a L.P.P. admits two optimal solutions then it has infinitely many optimal solutions.
Ans: d
Q 3) Solution set of inequality y ≥ 0 is
a) Half plane below x – axis excluding the points on the x – axis .
b) Half plane below x – axis including the points on the x – axis .
c) Half plane above x – axis .
d) None of these.
a) Half plane below x – axis excluding the points on the x – axis .
b) Half plane below x – axis including the points on the x – axis .
c) Half plane above x – axis .
d) None of these.
Ans: b
Q 4) Objective function of a L.P.P. is
a) Constraint
b) A function to be optimized
c) A relation between the variables.
d) None of these.
a) Constraint
b) A function to be optimized
c) A relation between the variables.
d) None of these.
Ans: b
Q 5) Which of the following terms is not used in a linear programming problems
a) Slack variable
b) Objective function
c) Convex region
d) Feasible region
a) Slack variable
b) Objective function
c) Convex region
d) Feasible region
Ans: d
Q 6) The point which does not lie in half plane 2x + 3y – 12 < 0 is
a) (1, 2)
b) (2, 1)
c) (2, 3)
d) (-3, 2)
a) (1, 2)
b) (2, 1)
c) (2, 3)
d) (-3, 2)
Ans: c
Q 7) Z = 7x + y, subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at
(a) (3, 0)
(b) (5, 6)
(c) (7, 0)
(d) (0, 5)
(a) (3, 0)
(b) (5, 6)
(c) (7, 0)
(d) (0, 5)
Ans: d
Q 8) 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)
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
a) p = 3q
b) p = 2q
c) p = q
d) q = 3p
Ans: d
Q 9) Z = 8x + 10y, subject to 2x + y ≥ 1, 2x + 3y ≥ 15, y ≥ 2, x ≥ 0, y ≥ 0. The minimum value of Z occurs at
(a) (4.5, 2)
(b) (1.5, 4)
(c) (0, 7)
(d) (7, 0)
(a) (4.5, 2)
(b) (1.5, 4)
(c) (0, 7)
(d) (7, 0)
Ans: b
Q 10) 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
a) p = q
b) p = 2q
c) q = 2p
d) q = 3p
Ans: d
Q 11) The solution set of the inequation 2x + y > 5 is
a) Half plane that contains the origin.
b) Open half plan not containing the origin.
c) Whole xy-plane except the point lying on the line 2x + y = 5
d) None of these
a) Half plane that contains the origin.
b) Open half plan not containing the origin.
c) Whole xy-plane except the point lying on the line 2x + y = 5
d) None of these
Ans: b
Q 12) The maximum value of f(x) = 4x + 3y subject to constraints x ≥ 0, y ≥ 0, 2x + 3y ≤ 18; x + y ≥ 10 is
(a) 35
(b) 36
(c) 34
(d) none of these
(a) 35
(b) 36
(c) 34
(d) none of these
Ans: d
Q 13) Which of the following statement is true
a) Every L.P.P. admits an optimal solution
b) An L.P.P admits a unique solution
c) If an L.P.P admits two optimal solutions, then it has an infinite number of optimal solutions.
d) An L.P.P admits only two optimal solution
a) Every L.P.P. admits an optimal solution
b) An L.P.P admits a unique solution
c) If an L.P.P admits two optimal solutions, then it has an infinite number of optimal solutions.
d) An L.P.P admits only two optimal solution
Ans: c
Q 14) Objective function of a L.P.P.is
(a) a constant
(b) a function to be optimized
(c) a relation between the variables
(d) none of these
(a) a constant
(b) a function to be optimized
(c) a relation between the variables
(d) none of these
Ans: b
Q 15) Objective function of a L.P.P is
a) a constant
b) a function to be optimized
c) a relation between the variable
d) None of these
a) a constant
b) a function to be optimized
c) a relation between the variable
d) None of these
Ans: b
Q 16) The objective function of Linear Programming Problem is
a) a polynomial
b) an equation
c) an inequation
d) None of these
a) a polynomial
b) an equation
c) an inequation
d) None of these
Ans: a
Q 17) The optimal value of the objective function is attained at the points
(a) on X-axis
(b) on Y-axis
(c) which are comer points of the feasible region
(d) None of these
(a) on X-axis
(b) on Y-axis
(c) which are comer points of the feasible region
(d) None of these
Ans: c
Q 18) The optimal value of the objective function is attained at the points
a) given by intersection of inequations with the axis only
b) given by intersection of inequations with x-axis only
c) given by corner points of the feasible region
d) None of these
a) given by intersection of inequations with the axis only
b) given by intersection of inequations with x-axis only
c) given by corner points of the feasible region
d) None of these
Ans: c
Q 19) Region represented by x ≥ 0, y ≥ 0 is
(a) first quadrant
(b) second quadrant
(c) third quadrant
(d) fourth quadrant
(a) first quadrant
(b) second quadrant
(c) third quadrant
(d) fourth quadrant
Ans: a
Q 20) The minimum value of P = 3x + y subject to 2x + 3y ≤ 6, x + y ≥ 1, x ≥ 0, y ≥ 0 is
a) 1/ 2
b) 0
c) 1
d) None of these
Ans: c
Q 21) The region represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 0, x ≥ 0, y ≥ 0 is
(a) unbounded
(b) a polygon
(c) exterior of a triangle
(d) None of these
Ans: d
Q 22) The maximum value of Z = 3x + 2y, subjected to x + 2y ≤ 2, x + 2y ≥ 8; x, y ≥ 0 is
(a) 32
(b) 24
(c) 40
(d) none of these
(a) 32
(b) 24
(c) 40
(d) none of these
Ans: d
Q 23) Maximize Z = 6x + 3y subject to x + y ≤ 5, x + 2y ≥ 4, 4x + y ≤ 12, x ≥ 0, y ≥ 0 is
a) 20
b) 21
c) 22
d) None of these
a) 20
b) 21
c) 22
d) None of these
Ans: c
Q 24) The minimum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5 + 2y ≥ 200, 2y ≥ 80; x, y ≥ 0 is
(a) 220
(b) 300
(c) 230
(d) none of these
Ans: a
(a) 220
(b) 300
(c) 230
(d) none of these
Ans: a
Q 25) Maximize Z = 11x + 8y, subject to x ≤ 4, 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)
(a) 44 at (4, 2)
(b) 60 at (4, 2)
(c) 62 at (4, 0)
(d) 48 at (4, 2)
Ans: b
Q 26) The feasible, region for an LPP is shown shaded in the figure. Let Z = 3x – 4y be the objective function. A minimum of Z occurs at
(a) (0, 0)
(b) (0, 8)
(c) (5, 0)
(d) (4, 10)
Ans: b
Q 27) 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)
(a) 16 at (4, 0)
(b) 24 at (0, 4)
(c) 24 at (6, 0)
(d) 36 at (0, 6)
Ans: d
Q 28) The conditions x ≥ 0, y ≥ 0 for LPP is called
a) Positive constraints
b) Non- negative constraints
c) Negative constraints
d) None of these
b) Non- negative constraints
c) Negative constraints
d) None of these
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