NTA UGC NET Linear Programming Problems Question with Solutions

Q1➡ | NTA UGC NET November 2020
i ➥ 23
ii ➥ 9.5
iii ➥ 13
iv ➥ 8

Show Answer With Best Explanation

Answer: IV
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q2➡ | NTA UGC NET December 2019
i ➥ x1=750, x2=750, z=1500
ii ➥ x1=500, x2=100, z=1500
iii ➥ x1=1000, x2=500, z=1500
iv ➥ x1=900, x2=600, z=1500

Show Answer With Best Explanation

Answer: III
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q3➡ | NTA UGC NET December 2019
Consider the following statements with respect to duality in LPP:
(a) The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself.
(b) If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution.
(c) If either problem has an unbounded optimal solution, then the other problem has no feasible solution at all. Which of the statements is (are) correct?
i ➥ only (a) and (b)
ii ➥ only (a) and (c)
iii ➥ only (b) and (c)
iv ➥ (a), (b) and (c)

Show Answer With Best Explanation

Answer: IV
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q4➡ | NTA UGC NET December 2019
A basic feasible solution of an mXn Transportation-Problem is said to be non-degenerate, if basic feasible solution contains exactly____number of individual allocation in ___positions
i ➥ m+n+1, independent
ii ➥ m+n-1, independent
iii ➥ m+n-1, appropriate
iv ➥ m-n+1, independent

Show Answer With Best Explanation

Answer: II
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q5➡ | NTA UGC NET JUNE 2019
i ➥ x1=5/2, x2=0, x3=0, Z=5
ii ➥ x1=0, x2=0, x3=5/2, Z=5
iii ➥ x1=0, x2=5/2, x3=0, Z= -5/2
iv ➥ x1=0, x2=0, x3=10, Z=20

Show Answer With Best Explanation

Answer: II
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q6➡ | NTA UGC NET December 2018
i ➥ x1 =2, x2 =0 and z = -4
ii ➥ x1 =2, x2 =6 and z = -22
iii ➥ x1 =0, x2 =2 and z = -6
iv ➥ x1 =6, x2 =2 and z = -18

Show Answer With Best Explanation

Answer: I
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q7➡ | NTA UGC NET JUNE 2018
Which of the following statements is false about convex minimization problem ?
i ➥ If a local minimum exists, then it is a global minimum
ii ➥ The set of all global minima is convex set
iii ➥ The set of all global minima is concave set
iv ➥ For each strictly convex function, if the function has a minimum, then the minimum is unique

Show Answer With Best Explanation

Answer: III
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q8➡ | NTA UGC NET JUNE 2018
The following LPP
Maximize z=100x1+2x2 +5x3
Subject to 14x1+x2 −6x3 +3x4 =7
32x1 +x2 −12x3 ≤10
3x1 −x2 −x3 ≤0
x1 , x2 , x3 , x4 ≥ 0
has
i ➥ x1 =100, x2 =0, x3 =0
ii ➥ Unbounded solution
iii ➥ No solution
iv ➥ x1 =50, x2 =70, x3 =60

Show Answer With Best Explanation

Answer: II
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q9➡ | NTA UGC NET November 2017 Paper -3
Which of the following is a valid reason for causing degeneracy in a transportation problem ?
Here m is no. of rows and n is no. of columns in transportation table
i ➥ When the number of allocations is m+n−1.
ii ➥ When two or more occupied cells become unoccupied simultaneously.
iii ➥ When the number of allocations is less than m+n−1.
iv ➥ When a loop cannot be drawn without using unoccupied cells, except the starting cell of the loop.

Show Answer With Best Explanation

Answer: III
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q10➡ | NTA UGC NET November 2017 Paper -3
Consider the following LPP :
Max Z = 15x1 + 10x2
Subject to the constraints
4x1 + 6x2 ≤ 360
3x1 + 0x2 ≤ 180
0x1 + 5x2 ≤ 200
x1, x2 / 0
The solution of the LPP using Graphical solution technique is :
i ➥ x1=60, x2=0 and Z=900
ii ➥ x1=60, x2=20 and Z=1100
iii ➥ x1=60, x2=30 and Z=1200
iv ➥ x1=50, x2=40 and Z=1150

Show Answer With Best Explanation

Answer: II
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q11➡ | NTA UGC NET November 2017 Paper -3
Consider the following LPP :
Min Z = 2x1 + x2 + 3x3
Subject to :
x1 − 2x2 + x3 ≥ 4
2x1 + x2 + x3 ≤ 8
x1 − x3 ≥ 0
x1, x2, x3 ≥ 0
The solution of this LPP using Dual Simplex Method is :
i ➥ x1=0, x2=0, x3=3 and Z=9
ii ➥ x1=0, x2=6, x3=0 and Z=6
iii ➥ x1=4, x2=0, x3=0 and Z=8
iv ➥ x1=2, x2=0, x3=2 and Z=10

Show Answer With Best Explanation

Answer: I (Marks to all )
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q12➡ | NTA UGC NET January 2017 Paper -3
Which of the following statements is true?
i ➥ The sentence S is a logical consequence of S1,…., Sn if and only if S1 ∧ S2 ∧…. ∧ Sn → S is satisfiable.
ii ➥ The sentence S is a logical consequence of S1,…., Sn if and only if S1 ∧ S2 ∧…. ∧ Sn → S is valid.
iii ➥ The sentence S is a logical consequence of S1,…., Sn if and only if S1 ∧ S2 ∧…. ∧ Sn → S is consistent.
iv ➥ The sentence S is a logical consequence of S1,…., Sn if and only if S1 ∧ S2 ∧…. ∧ Sn → S is inconsistent.

Show Answer With Best Explanation

Answer: II
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q13➡ | NTA UGC NET January 2017 Paper -3
A t-error correcting q-nary linear code must satisfy:

Where M is the number of code words and X is
i ➥ qn
ii ➥ qt
iii ➥ q-n
iv ➥ q-t

Show Answer With Best Explanation

Answer: I
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q14➡ | NTA UGC NET January 2017 Paper -3
With respect to a loop in the transportation table, which one of the following is not correct?
i ➥ Every loop has an odd no. of cells and at least 5.
ii ➥ Closed loops may or may not be square in shape.
iii ➥ All the cells in the loop that have a plus or minus sign, except the starting cell, must be occupied cells.
iv ➥ Every loop has an even no. of cells and at least four

Show Answer With Best Explanation

Answer: I
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q15➡ | NTA UGC NET January 2017 Paper -3
At which of the following stage(s), the degeneracy do not occur in transportation problem ? (m, n represents number of sources and destinations respectively)
(1) While the values of dual variables ui and vj cannot be computed.
(2) While obtaining an initial solution, we may have less than m + n – 1 allocations.
(3) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously.
(4) At a stage when the no. of +ve allocation is exactly m + n – 1.
i ➥ (a), (b) and (c)
ii ➥ (a), (c) and (d)
iii ➥ (a) and (d)
iv ➥ (a), (b), (c) and (d)

Show Answer With Best Explanation

Answer: III
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q16➡ | NTA UGC NET January 2017 Paper -3
Consider the following LPP :

The standard form of this LPP shall be :
i ➥
ii ➥
iii ➥
iv ➥

Show Answer With Best Explanation

Answer: I
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q17➡ | NTA UGC NET August 2016 Paper -3
Which of the following is used for the boundary representation of an image object?
i ➥ Quad Tree
ii ➥ Projections
iii ➥ Run length coding
iv ➥ Chain codes

Show Answer With Best Explanation

Answer: IV
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q18➡ | NTA UGC NET August 2016 Paper -3
The region of feasible solution of a linear programming problem has a _ property in geometry, provided the feasible solution of the problem exists.
i ➥ concavity
ii ➥ convexity
iii ➥ quadratic
iv ➥ polyhedron

Show Answer With Best Explanation

Answer: II
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q19➡ | NTA UGC NET August 2016 Paper -3
Consider the following statements:
(1) Revised simplex method requires lesser computations than the simplex method.
(2) Revised simplex method automatically generates the inverse of the current basis matrix.
(3) Less number of entries are needed in each table of revised simplex method than usual simplex method.
Which of these statements are correct?
i ➥ (1) and (2) only
ii ➥ (1) and (3) only
iii ➥ (2) and (3) only
iv ➥ (1), (2) and (3)

Show Answer With Best Explanation

Answer: IV
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q20➡ | NTA UGC NET August 2016 Paper -3
The following transportation problem: is

The above solution of a given transportation problem is:
i ➥ infeasible solution
ii ➥ optimum solution
iii ➥ non-optimum solution
iv ➥ unbounded solution

Show Answer With Best Explanation

Answer: II
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q21➡ | NTA UGC NET December 2015 Paper -3
A basic feasible solution of a linear programming problem is said to be __ if at least one of the basic variables is zero.
i ➥ Degenerate
ii ➥ non-degenerate
iii ➥ Infeasible
iv ➥ Unbounded

Show Answer With Best Explanation

Answer: I
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q22➡ | NTA UGC NET December 2015 Paper -3
Consider the following conditions:
(a)The solution must be feasible, i.e. it must satisfy all the supply and demand constraints.
(b)The number of positive allocations must be equal to m+n-1, where m is the number of rows and n is the number of columns.
(c)All the positive allocations must be in independent positions.
The initial solution of a transportation problem is said to be non-degenerate basic feasible solution if it satisfies:
i ➥ (a) and (b) only
ii ➥ (a) and (c) only
iii ➥ (b) and (c) only
iv ➥ (a), (b) and (c)

Show Answer With Best Explanation

Answer: IV
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q23➡ | NTA UGC NET December 2015 Paper -3
Consider the following transportation problem:

The transportation cost in the initial basic feasible solution of the above transportation problem using Vogel’s Approximation method is:
i ➥ 1450
ii ➥ 1465
iii ➥ 1480
iv ➥ 1520

Show Answer With Best Explanation

Answer: II
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q24➡ | NTA UGC NET June 2015 Paper -3
In the Hungarian method for solving assignment problem, an optimal assignment requires that the maximum number of lines that can be drawn through squares with zero opportunity cost is equal to the number of:
i ➥ rows or columns
ii ➥ rows + columns
iii ➥ rows + columns – 1
iv ➥ rows + columns + 1

Show Answer With Best Explanation

Answer: I
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q25➡ | NTA UGC NET June 2015 Paper -3
Given the following statements with respect to linear programming problem:
S1 : The dual of the dual linear programming problem is again the primal problem
S2 : If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution.
S3 : If either the primal or dual problem has a finite optimal solution, the other one also possesses the same, and the optimal value of the objective functions of the two problems are equal.
Which of the following is true?
i ➥ S1 and S2
ii ➥ S1 and S3
iii ➥ S2 and S3
iv ➥ S1 , S2 and S3

Show Answer With Best Explanation

Answer: IV
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

Q26➡ | NTA UGC NET June 2015 Paper -3
Consider the following transportation problem:

The initial basic feasible solution of the above transportation problem using Vogel’s Approximation Method (VAM) is given below:

The solution of the above problem.
i ➥ is degenerate solution
ii ➥ is optimum solution
iii ➥ needs to improve
iv ➥ is infeasible solution

Show Answer With Best Explanation

Answer: II
Explanation: Upload Soon

More DiscussionExplanation On YouTubeLearn Topic WiseHelp-Line

DO more practice

NTA UGC NET Subject Wise Previous Year Question With Solutions

error: Content is protected !!
Open chat
1
Hi,how Can We Help You ?