What does Game Theory study?
A Combinatorial optimization
B Graph theory
C Strategies in competitive situations
D Randomized algorithms
In graph theory, what is a bipartite graph?
A A graph with two disjoint sets of vertices
B A graph with cycles
C A graph with no edges
D A graph with a single vertex
What is a Nash equilibrium in Game Theory?
A A situation where one player wins
B A zero sum game
C A strategy where players collaborate
D A stable state where no player benefits from changing strategy
What is the main goal of cryptographic mathematics?
A To simplify mathematical problems
B To create secure communication systems
C To solve linear equations
D To model random events
What is an Eulerian circuit in a graph?
A A path that visits every edge exactly once
B A cycle that visits every vertex exactly once
C A path that visits every vertex
D A path with no cycles
What is a Hamiltonian cycle in a graph?
A A cycle that includes all vertices exactly once
B A path that covers only odd degree vertices
C A path that does not repeat vertices
D A path that covers all edges
What is the purpose of the Diffie Hellman key exchange algorithm?
A To generate random numbers
B To secure online transactions
C To exchange cryptographic keys securely
D To encrypt messages
In a graph, what is the degree of a vertex?
A The number of edges incident to it
B The number of vertices it connects to
C The number of paths to it
D The number of vertices in the graph
What is a key feature of an acyclic graph?
A It contains cycles
B It has no edges
C It has no cycles
D It has no cycles
What is the main idea behind randomized algorithms?
A They use random numbers to optimize solutions
B They work only with large data sets
C They use random numbers to optimize solutions
D They guarantee exact solutions
What is the concept of modular arithmetic used for?
A Multiplication
B Performing operations on remainders after division
C Solving polynomial equations
D Calculating factorials
What is the main purpose of an adjacency matrix in graph theory?
A To calculate graph’s degree
B To represent the graph using edges
C To store information about graph connectivity
D To store the distances between vertices
What is a complete graph?
A A graph with no edges
B A graph where every pair of vertices is connected
C A graph with exactly one cycle
D A graph with two sets of vertices
What does the principle of optimality in dynamic programming state?
A The problem can be solved by brute force
B The solution to the problem is built from solutions to subproblems
C Subproblems should not be solved independently
D A problem cannot be optimized
What does a directed acyclic graph (DAG) help represent in computer science?
A A network of nodes
B Relationships with cycles
C Data flow and dependencies
D Processes with no dependencies