TYBMS SEM 6 : Operation Research (Objective Questions with Solution)

 Paper/ Subject Code 86001/ Operation Research

TYBMS SEM 6 

Operation Research 

(Objective Questions with Solution)

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1) April 2019 Q.P. with Solution (PDF)

2) November 2019 Q.P. with Solution (PDF)

3) November 2022 Q.P. with Solution (PDF)

4) April 2023 Q.P. with Solution (PDF)

5) November 2023 Q.P. with Solution (PDF)

6) April 2024 Q.P. with Solution (PDF)

7) April 2025 Q.P. with Solution (PDF)

8) Objective Questions with Solution (PDF)

9) Most Important Write a Short Notes with Solution (PDF)

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April 2019

Q1.A) Multiple choice questions (Attempt Any 8)                                        (8)

[Video Explain Solution]

i) ln linear programming, unbounded solution means ____________. 

a) infeasible solution   b) Degenerate solution

c) Infinite solutions     d) Unique solution

 Ans: c) Infinite solutions

ii) If M + N-1 = Number of allocations in transportation, it means _________.

(Where 'M' is number of rows and N' is number of columns)

a) There is no degeneracy       b) Problem is unbalanced

c) Problem is degenerate        d) Solution is optimal

 Ans: a) There is no degeneracy  

iii) Floats for critical activities will be always _________________.

a) One             b) Zero

c) Highest        d) Same ás duration of the activity

 Ans: b) Zero

iv) The total time required to complete all the jobs-in a job sequencing problem is known as __________,

a) Idle time                              b) Processing time

c)Elapsed time                        d) Processing order

 Ans: c)Elapsed time

v) In linear programming, _____________ represents mathematical equation of the limitations imposed by the problem.

a) Objective function              b) Decision variable

c)Redundancy                         d) Constraints

Ans:  d) Constraints

vi) If in an assignment problem, number of rows is not equal to number of columns then ____________.

a) Problem is degenerate                                b) Problem is ‘unbalanced

c) It is a maximization problem                      d) Optimal solution is not possible

Ans:  b) Problem is ‘unbalanced

 vii) The maximum time in which an activity will be completed assuming all possible delays and postponements is termed as __________.

a) Optimistic time                   b) Most likely time

c) Pessimistic time                  d) Expected time

Ans: c) Pessimistic time

viii) The various alternatives or courses of actions available to each player in a game are called as __________.

a) Saddle points                      b) Strategies

c) Pay off                                d) 'n' player game

Ans: b) Strategies

ix) In simplex, a maximization problem is optimal when all Delta J, i.e., Cj-Zj values are

a) Either zero or positive                    b) Either zero or negative

c) Only positive                                  d) Only negative

Ans:   b) Either zero or negative

x) Which of the following considers difference between two least costs for each row and column while finding initial basic feasible solution in transportation?

a) North west corner rule                    b) Least cost method

c) Vogel's Approximation method       d) Row minima method

Ans:  b) Least cost method

Q1.B) True or false (Attempt Any 7)                                               (7)

i) Probability of a project completing in its expected time (Te) will be always 100%

Ans: False

ii) lf saddle point is available in a game, it is called as pure strategy game.

Ans: True

iii) Slack represents unutilized resources.

Ans: True

iv) If in a transportation problem, number of rows is not equal to number of columns, then the problem is unbalanced.

Ans: False

v) lf we introduce an unnecessary dummy activity, the error is termed as redundancy.

Ans: True

vi) Job sequencing problems are solved to ensure that, both, the total time to complete all jobs and idle time of each machine are maximum.

Ans: False

vii) When more than one optimal solution is possible in a linear programming problem, it is termed as 'unique solution'.

Ans: False

viii) Regret matrix is made to convert a maximization problem into minimization problem in assignment.

Ans: True

ix) Critical path method (CPM) considers the three-time estimates: most likely, optimistic and pessimistic time estimates.

Ans: False

x) In solving a job sequencing problem, it is assumed that all jobs require the same sequence of operations.

Ans: False

November 2019

Q.1A) Match the right and closely related answer from Column Y with the text / term given in Column X. ( Attempt Any 7 questions )

Column X	Column Y
1) Value of Game = 0	a) Training programme scheduling
2) Optimistic Time	b) If no. of Row > No. of Columns
3) Application of O.R. in HRM	c) Minimization types transportation problem
4) Pessimistic Time	d) Does not affect the feasible solution
5) Add Dummy Row in Assignment	e) To maximize per capita income
6) Redundant Constraint in Graphical	f) one player’s gain is the other player’s Loss
7) Application of O.R. in Finance	g) If no. of Row < No. of Columns
8) Transportation elements as time	h) fair game
9) Add Dummy Column in Assignement	i) Shortest and ideal Time estimate in PERT
10) Zero Sum Game	j) Time estimate in PERT by considering worst delays

ANS :

Column X	Column Y
1) Value of Game = 0	f) one player’s gain is the other player’s Loss
2) Optimistic Time	i) Shortest and ideal Time estimate in PERT
3) Application of O.R. in HRM	a) Training programme scheduling
4) Pessimistic Time	j) Time estimate in PERT by considering worst delays
5) Add Dummy Row in Assignment	g) If no. of Row < No. of Columns
6) Redundant Constraint in Graphical	d) Does not affect the feasible solution
7) Application of O.R. in Finance	e) To maximize per capita income
8) Transportation elements as time	c) Minimization types transportation problem
9) Add Dummy Column in Assignement	b) If no. of Row > No. of Columns
10) Zero Sum Game	h) fair game

Q.1 B) State whether following statements True or False: (Attempt any 8)                             (8)

1) One of the areas of application of Operations Research is in Agriculture.

Ans: False

2) A linear programming model consists of only decision variables and constraints

Ans: True

3) In graphical method of LPP the optimum value occurs anywhere in feasible region.

Ans: True

4) If the assignment elements are cost elements then the objective of the optimal assignment is to maximize the cost.

Ans: False

5) In transportation problem, number of basic allocated (or Occupied) cells should be exactly m+n+1, so that it becomes non-degenerate.

Ans: False

6) Dummy activity does not consume time or resources.

Ans: True

7) The three time estimates employed in PERT are: optimistic time, average expected time, and pessimistic time.

Ans: True

8) In Sequencing the time taken by each job in changing over from one machine to another is negligible.

Ans: False

9) The row [-1,10, 20] dominates the row [0,0,0]

Ans: False

10) The column [0,-1,-2] dominates the column [0,-1, -1]

Ans: False

November 2022

Q.1 A) State whether following statements True or False:(Attempt any8)         (8)

Video Solution Q.1 (a/b)

1. Operation Research, Methodology consists of definition, solution and validation only.

Ans: False. Operation Research methodology typically involves problem formulation, model construction, solution, validation, and implementation phases.

2. A linear programing problem may have more than one set of solutions.

Ans: True. A linear programming problem can have multiple solutions, especially if the feasible region is unbounded.

3. In graphical method of LPP, if the objective function is parallel to a constraints, the constraint is infeasible. 

Ans: False. If the objective function is parallel to a constraint line in the graphical method of linear programming, it means the constraint is redundant or there are infinite feasible solutions, not necessarily infeasible.

4. It is possible for an equation in the simplex table to have both a slack and surplus variable at the same time 

Ans: False. In the simplex method, an equation in the simplex table cannot have both a slack and a surplus variable at the same time because they represent different types of variables.

5. The Hungarian method for solving an assignment problem can also be used to solve a transportation problem.

Ans: True. The Hungarian method, which is an algorithm for solving the assignment problem, can be adapted to solve transportation problems.

6. Regret matrix is made to convert a maximization problem into minimization problem in assignment. 

Ans: True. The regret matrix is used in decision theory to assess the consequences of different decisions, but it doesn't necessarily convert a maximization problem into a minimization problem.

7. In transportation problem, number of basic allotted (or Occupied) cells should be exactly m + n + 1 that it becomes non-degenerate.

Ans: False. The number of basic allotted cells in a transportation problem should be exactly m + n - 1, where m is the number of sources and n is the number of destinations, to ensure non-degeneracy.

8. In PERT, the total project completion time follows a normal probability distribution.

Ans: False. In PERT (Program Evaluation and Review Technique), the total project completion time follows a beta distribution, not a normal distribution.

9. The orders of completion of jobs are dependent on the sequence of jobs. 

Ans: True. The order of completion of jobs can be dependent on the sequence of jobs in certain scheduling problems.

10. Different saddle points in the same payoff matrix always have the same payoff.

Ans:  False. Different saddle points in the same payoff matrix can have different payoffs.

Q.1. (B) Match the right and closely related answer from Column Y with the text/term given in Column X. (Attempt Any 7 question) (7)

Column X	Column Y
1) Key Column	a) Method of penalties
2) feasible region	b) Crash cost per day
3)VAM Method	c) Region of feasible solution
4) Dummy Row or Column	d) Incoming variable in Simplex
5) NWCR	e) LST-EST or LET-EFT
6) Cost Slope in Crashing	f) Optimistic time
7) Total Float value	g) Saddle point not available in the game
8) Shortest activity time in PERT	h) Unbalance problem
9) Mixed strategy game	i) Time required by a job or any machine
10) Processing time	j) Top left side corner of the side

Ans: 

Column X	Column Y
1) Key Column	d) Incoming variable in Simplex
2) feasible region	c) Region of feasible solution
3)VAM Method	a) Method of penalties
4) Dummy Row or Column	h) Unbalance problem
5) NWCR	j) Top left side corner of the side
6) Cost Slope in Crashing	b) Crash cost per day
7) Total Float value	e) LST-EST or LET-EFT
8) Shortest activity time in PERT	f) Optimistic time
9) Mixed strategy game	g) Saddle point not available in the game
10) Processing time	i) Time required by a job or any machine

April 2023

Q.1 A) State whether following statements True or False:(Attempt any8)         (8)

Video Solution Q.1 (a/b)  

1) Operation research is also termed as management science.

Ans: True

2) The objective function is a linear relationship reflecting the objective of an operation.

Ans:  False

3) The feasible region is a convex set.

Ans: True

4) the value of ∆j = Cj -- Zj row in the simplex table tells us whether the current solution is optimal, and, if it is not, what variable will be in the optimal solution.

Ans: False

5) if the assignment elements are cost elements,  then the objective of the optimal assignment is to maximize the cost. 

Ans: False

6) MODI method is the best method to get initials feasible transportation solution.

Ans: True

7) the dummy activity has an expected time of zero by definition. 

Ans: True

8 ) the PERT pessimistic time estimate is an estimate of the minimum time an activity will require. 

Ans: True

9) in solving a job sequencing problem, it is assumed that all jobs require the same sequencing of operations.

ANS: False

10) if saddle point is available in a game, it is called as pure strategy game.             

Ans: True

Q.1B) Match the right and closely related answer from Column Y with the text / term given in Column X. ( Attempt Any 7 questions )

Column X	Column Y
1) Leaner relationship of Variable	a) Completely utilized resources
2) Infeasible region	b) Minimum cost in the table
3) Scarce resource	c) No feasible solution Possible
4) LCM	d) LPP
5) NWCR	e) In the game, gains of the winner are equal to total losses of all other players
6) Critical Activity	f) Optimistic time
7) Zero sum game	g) Fair game
8) Shortest activity time in PERT	h) Zero float value
9) Value of game =0	i) The time during which a machine is waiting or not working
10) Ideal time	j) Top left side corner of the side

 

Ans: 

Column X	Column Y
1) Leaner relationship of Variable	d) LPP
2) Infeasible region	c) No feasible solution Possible
3) Scarce resource	a) Completely utilized resources
4) LCM	b) Minimum cost in the table
5) NWCR	j) Top left side corner of the side
6) Critical Activity	h) Zero float value
7) Zero sum game	e) In the game, gains of the winner are equal to total losses of all other players
8) Shortest activity time in PERT	f) Optimistic time
9) Value of game =0	g) Fair game
10) Ideal time	i) The time during which a machine is waiting or not working

November 2023

Q.1 Multiple Choice Questions: (Attempt Any 8)                (8)

Click Here

1. Operation research, which is very powerful tool for ________.

a) Research

b) Decision Making

c) Operations

d) None of the above

2. Constraints in LPP model represent ________. 

a) Limitations

b) Requirement

c) Balancing limitations and requirements

d) All of the above

3. While solving a LP model graphically, the area bounded by the constraints is called ________.

a) Feasible region

b) Infeasible region

c) Unbounded solution

d) None of the above

4. For solving an assignment problem, which method is used ?

a) British

b) American

c) German

d) None of the above

5. The solution to a transportation problem with m' rows (supplies) & n columns (destination) is feasible if number of positive allocations are

a) m*n

b) m-n

c) m-n-1

d) m+n-l

6. When total supply doesn't match with total demand ________. case exists a transportation problem.

a) unbalanced

b) alternate optimal solution

c) degeneracy

d) none of the above

7. Floats for critical activities will be always ________.

a) zero

b) backward

c) > 1

d) none of the above

8.The two types of costs involved in the process of crashing in a project are costs.

a) direct and indirect

b) partial and full

c) measurable and non-measurable

d) none of these

9. The various courses of actions available to each player are called as

a) Saddle points

b) strategies

c) Pay-offs

d) n player game

10. The total time required to complete all the job-sequencing problem is known as

a) idle time

b) processing time

c) elapsed time

d) processing time

Q.1 B) Match the following (Any Seven)                (7)

Group A	Group B
1 Network scheduling	a) Marketing. Finance
2. Application of OR	b) PERT and CPM
3. Linear programming	c. Worker's allocation
4 Assignment problem	d) Quantitative in nature
5 OR techniques	e. Maximizing minimizing objective function
6. MODI method	f) No of columns to of rows
7. Add dummy row	g) At the start
8. Crash Cost per day	h) Feasible solution
9. Pure strategy game	1) Cost slope
10. A job with smallest processing time on machine A is placed	j) Saddle point exits

 Ans: 

Group A	Group B
1 Network scheduling	b) PERT and CPM
2. Application of OR	a) Marketing. Finance
3. Linear programming	e) Maximizing minimizing objective function
4 Assignment problem	c) Worker's allocation
5 OR techniques	d) Quantitative in nature
6. MODI method	h) Feasible solution
7. Add dummy row	f) No of columns to of rows
8. Crash Cost per day	i) Cost slope
9. Pure strategy game	j) Saddle point exits
10. A job with smallest processing time on machine A is placed	g) At the start

 

April 2024

Q1 (A) Multiple choice questions (Attempt Any 8):    (8)

Click Here for Solution

1. A BFS of a LPP is said to be _______ if at least one of the basic variables is zero

a) Degenerated 

b) Non-degenerated 

c) Infeasible 

d) Feasible

2 . For solving an assignment problem, which method is used?

a) Hungarian

b) American

c) German

d) Italian

3. A feasible solution is called a basic feasible solution if the number of non-negative allocations is equal to _______.

a) m-n+1

b) m-n-1

c) m-n-1

d) m+n-1

4. Which method is an iterative procedure for solving LPP in a finite number of steps

a) Simplex algorithm

b) Simplex method

c) slack method

d) M-method

5. An objective function is maximized when it is a ________ function.

a) Profit

b) passive

c) cost

d) time

6. In an assignment problem involving 5 workers & 5 jobs, the total number of assignments possible is

a) 15

b) 10

c) 5

d) 20

7. is known as the time by which activity completion time can be delayed without affecting the start of succeeding activities,

a) Total float

b) interfering float

c) independent float

d) Free float

8. The probability of a normal curve is ________

a) 60%

b) 70%

c) 50%

d) 55%

9. What is the probability of project completing in 55 days if the expected project completion time is 47 days & table value is :(+0.4890)

a) 98.90% 

b) 99% 

c) 90% 

d)98%

10. What is the total idle time if jobs are processed on 2 machines and idle time on machine A is 11 and on machine B is 15.

a) 25

b) 26

c) 23

d) 24

Q1 (B) True or false (Attempt Any 7) operation:    (7)

i. concerned with using scientific approach i.e. logical reasoning to solve problems for the management by ensuring optimum utilization of resources

Ans: TRUE 

Linear programming is indeed concerned with using a scientific approach (logical reasoning) to solve problems for management by ensuring optimal utilization of resources. It's a mathematical method to find the best outcome (maximum profit, minimum cost, etc.) considering constraints.

ii. Any change in the constraint inequalities will have a proportional change in the objective function

Ans: FALSE  

Changes in constraint inequalities won't necessarily result in a proportional change in the objective function. The relationship between constraints and the objective function is linear, but the impact of a change depends on the specific constraints and objective function being optimized.

iii. In graphical method, infeasibility happens we cannot find feasible region.

Ans: TRUE. 

In the graphical method of LP, infeasibility occurs when there's no intersection between the constraint lines, indicating no feasible region that satisfies all constraints simultaneously.

iv. Graphical method can be used when the number of decision variable at two

Ans: FALSE 

The graphical method can be used for problems with more than two decision variables, although it becomes cumbersome to visualize as the number of variables increases. For higher dimensions, the simplex method is a more efficient solution technique.

V An artificial variable is a fictitious variable in LPP problems.

Ans: TRUE  Artificial variables are fictitious variables introduced in the simplex method (a common LP technique) to convert an infeasible LP problem into a feasible one for initial calculations. They are eventually removed from the optimal solution.

vi. Surplus variables represent an excess amount of resources utilize

Ans: TRUE Surplus variables represent the unused amount of resources (slack) in a constraint. They are non-negative in the optimal solution and indicate how much a constraint can be relaxed without affecting the objective function.

vii . When the number of lines is not equal to size of matrix the solution is optimum.

Ans: FALSE  The number of lines (constraints) not being equal to the size of the matrix doesn't guarantee an optimal solution. There are specific conditions for optimality in LP, and this statement doesn't provide a sufficient criterion.

viii. There are two types of techniques available to find the initial basic feasible solution.

Ans: TRUE  There are two main methods to find the initial basic feasible solution in the simplex method: the Northwest corner method and the least-cost method (also known as Vogel's approximation method). Both methods provide a starting point for the iterative optimization process.

ix. The network can have one or more start node and end node.

Ans: TRUE  A network in LP (network simplex method) can have one or more source nodes (representing starting points with available resources) and one or more destination nodes (representing goals to be achieved).

X. Pessimistic time is the shortest time period expected to complete the activity.

Ans: FALSE Pessimistic time refers to the longest expected time to complete an activity, not the shortest. It's a concept used in project management, particularly in PERT (Program Evaluation and Review Technique), to estimate project durations considering potential delays.

April 2025

Q1 A) State whether following Statements are True or False (Any Eight):        (08)

1. Linear Programming Problems consist of decision variables, an objective function, and constraints.

Ans: True

2. In the Graphical Method of Linear Programming, the feasible region is always a polygon.

Ans: True

3. The Assignment Problem can have multiple optimal solutions.

Ans: True

4. In a balanced transportation problem, the total supply must be equal to the total demand.

Ans: True

5. Dummy activities are used in network diagrams to maintain logical dependencies

Ans: True

6. The Program Evaluation and Review Technique (PERT) considers three time estimates for activity duration.

Ans: True

7. Crashing a project reduces both time and cost simultaneously.

Ans: False

8. In job sequencing, idle time refers to the time a machine remains unutilized.

Ans: True

9. A two-person zero-sum game means that one player's gain is exactly equal to the other player's loss.

Ans: True

10. In the Simplex Method, slack variables are introduced to convert inequalities into equations. 

Ans: True

QI B) Match the Column Questions: (Any SEVEN)                (07)

Column A	Column B
1. Feasible Region	a) Method to solve transportation problems
2. Redundant Constraint	b) Project scheduling technique
3. Decision Variables	c) Represents unused or excessive restrictions in LPP
4. Unbounded Solution	d) Graphical area satisfying all constraints in LPP
5. Duality in Linear Programming	e) Used in Linear Programming Formulation
6. MODI Method	f) When there is no finite optimal solution
7. Slack Variable	g) Difference between primal and dual problems
8. Network Diagram	h) Extra variable added to convert "<" constraint into equality
9. Zero-Sum Game	i) One player's gain is equal to the other player's loss
10. Least Cost Method (LCM)	j) Heuristic approach for transportation problems

Ans:

Column A	Column B
1. Feasible Region	d) Graphical area satisfying all constraints in LPP
2. Redundant Constraint	c) Represents unused or excessive restrictions in LPP
3. Decision Variables	e) Used in Linear Programming Formulation
4. Unbounded Solution	f) When there is no finite optimal solution
5. Duality in Linear Programming	g) Difference between primal and dual problems
6. MODI Method	a) Method to solve transportation problems
7. Slack Variable	h) Extra variable added to convert "<" constraint into equality
8. Network Diagram	b) Project scheduling technique
9. Zero-Sum Game	i) One player's gain is equal to the other player's loss
10. Least Cost Method (LCM)	j) Heuristic approach for transportation problems

November 2025

Q.1 A State whether the following statements are True or False (Attempt any 8): (08)

1. Operation Research is also termed as Management Science.

Ans: True

2 All LPP can be solved using graphical solution.

Ans: False

3. The feasible region is convex set.

Ans: True

4. The key column is determined by higher positive value of Aj - zj

Ans: True

5. If sadder point is available in a game it is called as pure strategy game.

Ans: True

6. We use Hungarian method to solve assignment problem.

Ans: True

7. Regret matrix is made to convert the maximization problem into minimization problem in assignment problem.

Ans: True

8) PERT stands for program efficiency and review techniques.

Ans: False

9) EST Stands for earliest start time of any activity.

Ans: True

10) A job starts on machine as soon as the job end the machine both are idle.

Ans: False

Q.1 B Match the right and closely related answer from column Y with the text term given in column X (Attempt any seven questions):            (07)

Column X	Column Y
1.Optimal job sequence	a) Time estimates import by considering worst delays.
2. Maximin strategy	b) Coefficient of the variable in the objective function.
3. Principle of dominance	c) Minimum total elapsed time
4. Total flute	d) Production scheduling problem
5. Pessimistic time	e) Reduction in order of matrix
6. Maximum crashing possible	f) Player one should select the strategy whose minimum payoff to player 2 is largest
7. Cj row	g) latest start time - earliest start time
8. Feasible solution	h) Normal Time - crash Time
9. Industrial application of OR	i) Vogel's approximation method
10.VAM stand for	j) Solution for which all constraints are satisfied

Ans:

Column X	Column Y
1.Optimal job sequence	c) Minimum total elapsed time
2. Maximin strategy	f) Player one should select the strategy whose minimum payoff to player 2 is largest
3. Principle of dominance	e) Reduction in order of matrix
4. Total flute	g) latest start time - earliest start time
5. Pessimistic time	a) Time estimates import by considering worst delays.
6. Maximum crashing possible	h) Normal Time - crash Time
7. Cj row	b) Coefficient of the variable in the objective function.
8. Feasible solution	j) Solution for which all constraints are satisfied
9. Industrial application of OR	d) Production scheduling problem
10.VAM stand for	i) Vogel's approximation method