**1. What does the M/M/1 notation represent in waiting line models?**

a) Multiple servers with exponential service times

b) Single server with exponential service times

c) Multiple servers with constant service times

d) Single server with constant service times

**Answer: b) Single server with exponential service times**

Explanation: In waiting line models, M/M/1 signifies a single-server system where arrivals and service times follow exponential distributions.

**2. Which factor is crucial for determining the average length of customers in an M/M/1 queue?**

a) Arrival rate

b) Service rate

c) Number of servers

d) Queue discipline

**Answer: a) Arrival rate**

Explanation: The average length of customers in an M/M/1 queue heavily depends on the rate at which customers arrive.

**3. What is the optimum service rate in an M/M/1 queue system?**

a) Equal to the arrival rate

b) Equal to half of the arrival rate

c) Greater than the arrival rate

d) Independent of the arrival rate

**Answer: c) Greater than the arrival rate**

Explanation: The optimum service rate in an M/M/1 queue system is greater than the arrival rate to prevent infinite queue growth.

**4. In a multiple-server model (M/M/s), what does ‘s’ represent?**

a) Number of servers

b) Arrival rate

c) Service rate

d) Queue size

**Answer: a) Number of servers**

Explanation: ‘s’ in the M/M/s model denotes the number of servers available to serve customers concurrently.

**5. What is a competitive strategy in game theory?**

a) A strategy aimed at cooperation

b) A strategy to dominate opponents

c) A strategy focused on minimizing losses

d) A strategy aimed at outperforming others

**Answer: d) A strategy aimed at outperforming others**

Explanation: A competitive strategy in game theory involves making decisions to achieve an advantage over other participants.

**6. Which method can be used to solve two-person zero-sum games graphically?**

a) Simplex method

b) Linear programming

c) Dominance

d) Payoff matrix

**Answer: d) Payoff matrix**

Explanation: Two-person zero-sum games can be solved graphically using a payoff matrix, where each player’s strategies and payoffs are outlined.

**7. What is a pure strategy in game theory?**

a) A strategy involving random choices

b) A strategy based on mixed actions

c) A deterministic strategy

d) A strategy aimed at cooperation

**Answer: c) A deterministic strategy**

Explanation: A pure strategy in game theory involves selecting a specific action with certainty, without incorporating random elements.

**8. In game theory, what does dominance refer to?**

a) Strategy that always yields the highest payoff

b) Strategy that eliminates all opponents

c) Strategy that guarantees a win

d) Strategy that is always better regardless of opponents’ choices

**Answer: d) Strategy that is always better regardless of opponents’ choices**

Explanation: Dominance in game theory refers to a strategy that is superior to others regardless of opponents’ choices.

**9. What does LP stand for in solving game theory problems?**

a) Linear Probability

b) Linear Performance

c) Linear Programming

d) Limited Play

**Answer: c) Linear Programming**

Explanation: LP stands for Linear Programming, a method used to solve various optimization problems, including those in game theory.

**10. In a two-person zero-sum game, what is a saddle point?**

a) A point of equilibrium

b) A point of maximum payoff

c) A point of minimum payoff

d) A point of dominance

**Answer: a) A point of equilibrium**

Explanation: In a two-person zero-sum game, a saddle point is a point of equilibrium where neither player has an incentive to change their strategy.

**11. What assumption is commonly made in waiting line models regarding service times?**

a) Exponential distribution

b) Constant distribution

c) Normal distribution

d) Poisson distribution

**Answer: a) Exponential distribution**

Explanation: Waiting line models often assume that service times follow an exponential distribution, allowing for mathematical tractability.

**12. In game theory, what does a mixed strategy involve?**

a) Using a combination of deterministic actions

b) Randomly selecting strategies

c) Collaborating with opponents

d) Eliminating opponents

**Answer: a) Using a combination of deterministic actions**

Explanation: A mixed strategy in game theory involves using a combination of deterministic actions to create uncertainty for opponents.

**13. What factor is crucial for determining the average time a customer spends in a waiting line?**

a) Service rate

b) Arrival rate

c) Queue discipline

d) Number of servers

**Answer: c) Queue discipline**

Explanation: The average time a customer spends in a waiting line is influenced by the discipline followed in managing the queue, such as first-come-first-served or priority-based.

**14. Which method is used to solve game theory problems algebraically?**

a) Dominance

b) Payoff matrix

c) Linear programming

d) Graphical method

**Answer: c) Linear programming**

Explanation: Game theory problems can be solved algebraically using techniques like linear programming to optimize strategies and outcomes.

**15. What does the ‘M’ represent in M/M/s waiting line models?**

a) Maximum queue size

b) Minimum service time

c) Markovian property

d) Maximum arrival rate

**Answer: c) Markovian property**

Explanation: In M/M/s waiting line models, the ‘M’ signifies the Markovian property, where the next state of the system depends only on its current state, not its history.