MULTIPLE CHOICE QUESTIONS. 1) Let A and B be any two arbitrary events then which one of the following is true?

Transcription

1 DISCRETE SRUCTURES MULTIPLE CHOICE QUESTIONS 1) Let A and B be any two arbitrary events then which one of the following is true? a. P( A intersection B) = P(A). P(B) b. P(A union B) = P(A) + P(B) c. P(AB) = P(A intersection B). P(B) d. P(A union B) >= P(A) + P(B) 2) If X and Y be the sets. Then the set ( X - Y) union (Y- X) union (X intersection Y ) is equal to? a. X union Y b. X c union Y c c. X intersection Y d. X c intersection Y c 3) If G is an undirected planer graph on n vertices with e edges then? a. e<=n b. e<=2n c. e<=3n 4) Which of the following statement is false? a. G is connected and is circuitless b. G is connected and has n edges c. G is minimally connected graph d. G is circuitless and has n-1 edges

2 5) Probability that two randomly selected cards from a set of two red and two black cards are of same color is? a. 1 / 2 b. 1 / 3 c. 2 / 3 6) The number of circuits that can be created by adding an edge between any two vertices in a tree is? a. Two b. Exactly one c. At least two d. None 7) In a tree between every pair of vertices there is? a. Exactly one path b. A self loop c. Two circuits d. n number of paths 8) The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from some same suit is? a. 8 b. 3 c. 9 d. 12 Answer = C 9) Context free languages are closed under?

3 a. union, intersection b. Intersection, complement c. union, kleene star d. Complement, kleene star Answer = C 10) Let R be a symmetric and transitive relation on a set A. Then? a. R is reflexive and hence a partial order b. R is reflexive and hence an equivalence relation c. R is not reflexive and hence not an equivalence relation d. None of above 11) Context free Grammar is? a. A Compiler b. A language expression c. A regular expression Explanation: Context free Grammar generate the context free languages. These are defined by the rule of the form A -> b Where Aanon terminal and b is the string of terminals. 12) The idea of an automation with a stack as auxiliary storage...? a. Finite automata b. Push down automata c. Deterministic automata Explanation: Push down automata manipulate the stack, as a part of performing a transition. 13) A Pushdown automata is...if there is at most one transition applicable to each configuration?

4 a. Deterministic b. Non Deterministic c. Finite d. Non Finite Explanation:If in every situation only one transition is available as continuation of computation, then the result is a deterministic push down automation (DPDA). 14) The graphical representation of the transition of finite automata is? a. Finite diagram b. State diagram c. Node diagram d. E-R diagram Explanation: State diagram is called the graphical representation of Finite automata. 15) If two sets A and B have no common elements i.e (A intersection B) has no element then such sets are known as? a. Intersection b. Union c. Disjoint d. Complement Answer = C Explanation:If two sets have no element in common then they are called disjoint sets. 16) The domain D of the relation R is defined as the...? a. Set of all elements of ordered pair which belongs to R b. Set of all last elements of ordered pair which belongs to R c. Set of all first elements of ordered pair which belongs to R

5 Answer = C 17) 'A language is regular if and only if it is accepted by a finite automation'? a. The given statement is true b. The given statement is false c. The given statement is partially true d. Sometime true, sometimes false Explanation: A regular language is accepted by the finite automation. Every regular language is context free. 18) Which of the following does not belong to the context free grammer? a. Terminal symbol b. Non-terminal symbol c. Start symbol d. End symbol Explanation:Context free grammar consist of terminal symbols, non terminal symbols, set of production rules, a start symbol but does not have any End symbol. 19) A regular grammar is a...? a. Context free grammar b. Non context free grammar c. English grammar d. None of above Explanation: Regular grammar is context free grammar. Such a grammar restricts its rules to a single non terminal on the left hand side and right hand side consisting of a single terminal. 20) The context free language are closed under...? a. Union

6 b. Kleene star c. Concatenation d. All of above Explanation: Context free language is closed under union, kleene star and concatenation. 21) A graph is a collection of...? a. Row and columns b. Vertices and edges c. Equations Explanation: A graph contains the edges and vertices 22) The degree of any vertex of graph is...? a. The number of edges incident with vertex b. Number of vertex in a graph c. Number of vertices adjacent to that vertex d. Number of edges in a graph Explanation: The number of edges connected on a vertex v with the self loop counted twice is called the degree of vertex. 23) If for some positive integer k, degree of vertex d(v)=k for every vertex v of the graph G, then G is called...? a. K graph b. K-regular graph c. Empty graph d. All of above

7 Explanation: A graph in which all vertices are of equal degree is called regular graph. 24) A graph with no edges is known as empty graph. Empty graph is also known as...? a. Trivial graph b. Regular graph c. Bipartite graph Explanation: Trivial graph is the second name for empty graph. 25) Length of the walk of a graph is...? a. The number of vertices in walk W b. The number of edges in walk W c. Total number of edges in a graph d. Total number of vertices in a graph Explanation: A walk is defined as finite altering sequence of vertices and edges. No Edges appear more than once but vertex may appear more than once. 26) If the origin and terminus of a walk are same, the walk is known as...? a. Open b. Closed c. Path Explanation: A walk which begins and ends with same vertex is called closed walk otherwise it is open. 27) A graph G is called a...if it is a connected acyclic graph?

8 a. Cyclic graph b. Regular graph c. Tree d. not a graph Answer = C 28) Eccentricity of a vertex denoted by e(v) is defined by...? a. max { d(u,v): u belongs to v, u does not equal to v : where d(u,v) is the distance between u&v} b. min { d(u,v): u belongs to v, u does not equal to v } c. Both A and B Explanation: The eccentricity E(v) of a vertex V in the graph is the distance from v to the vertex farthest from v in G. 29) Radius of a graph, denoted by rad(g) is defined by...? a. max {e(v): v belongs to V } b. min { e(v): v belongs to V} c. max { d(u,v): u belongs to v, u does not equal to v } d. min { d(u,v): u belongs to v, u does not equal to v } Explanation: The diameter or radius of a graph G is largest distance between two vertices in the graph G. 30) The complete graph K, has... different spanning trees? a. n n-2 b. n*n c. n n d. n 2

9 31) A tour of G is a closed walk of graph G which includes every edge G at least once. A...tour of G is a tour which includes every edge of G exactly once? a. Hamiltonian b. Planar c. Isomorphic d. Euler Explanation: If some closed walk in a graph contains all the edges then the walk is called Euler. 32) Which of the following is not a type of graph? a. Euler b. Hamiltonian c. Tree d. Path Explanation:Path is a way from one node no another but not a graph. 33) Choose the most appropriate definition of plane graph? a. A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices b. A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non - empty disjoint subset X and Y in such a way that each edge of G has one end in X and one end in Y. c. A simple graph which is Isomorphic to Hamiltonian graph 34) A continuous non - intersecting curve in the plane whose origin and terminus coincide? a. Planer

10 b. Jordan c. Hamiltonian d. All of these Explanation: The jordan graph is the set of all vertices of minimum eccentricity that is the set of all vertices A where the greatest distance to other vertex B is minimal. 35) Polyhedral is...? a. A simple connected graph b. A plane graph c. A graph in which the degree of every vertex and every face is atleast 3 d. All of above Explanation: A polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron 36) A path in graph G, which contains every vertex of G once and only once? a. Eulartour b. Hamiltonian Path c. Eular trail d. Hamiltonian tour Explanation:A Hamiltonian circuit in a connected graph is defined as a closed walk that traverse every vertex of G exactly once except the starting vertex. 37) A minimal spanning tree of a graph G is...? a. A spanning sub graph b. A tree c. Minimum weights d. All of above

11 Explanation: A tree is said to be spanning tree of connected graph G if it is subgraph of G and contains all the vertices of G. 38) A tree having a main node, which has no predecessor is...? a. Spanning tree b. Rooted tree c. Weighted tree Explanation:A tree in which one vertex distinguish from all other is called rooted tree. 39) Diameter of a graph is denoted by diam(g) is defined by...? a. max (e(v) : v belongs to V) b. max( d(u,v) ) c. Both A and B Answer = C Explanation: The diameter of a graph G is largest distance between two vertices in a graph G. 40) A vertex of a graph is called even or odd depending upon? a. Total number of edges in a graph is even or odd b. Total number of vertices in a graph is even or odd c. Its degree is even or odd Answer = C Explanation: The vertex of a graph is called even or odd based on its degree.

12 41) If the sequence of operations - push(1), push(2), pop, push(1), push(2), pop, pop, pop, push(2), pop are performed on a stack, the sequence of popped out values are? a. 2, 2, 1, 1, 2 b. 2, 2, 1, 2, 2 c. 2, 1, 2, 2, 1 d.2, 1, 2, 2, 2 Explanation: The elements are popped from the top of the stack. 42) Queue can be used to implement? a. radix sort b. quick sort c. recursion d. depth first search Explanation: A simple version of an LSD radix sort can be achieved using queues as buckets. 43) A machine took 200 sec to sort 200 names, using bubble sort. In 800 sec, it can approximately sort? a. 400 names b. 800 names c. 750 names d. 800 names Explanation:For sorting 200 names bubble sort makes 200 x 199/2 = comparisons. The time needed for 1 comparison is 200 sec. In 800 sec it can make 80,000 comparisons. We have to fine n, such that n(n - 1)/2 = 80,000. From this n is approximately 400.

13 44) A machine needs a minimum of 100 sec to sort 1000 names by quick sort.the minimum time needed to sort 100 names will be approximately? a sec b. 6.7 sec c sec d sec Explanation: In the best case quick sort algorithm makes n log(n) comparisons. so 1000 x log (1000) = 9000 comparisons, which takes 100 sec. To sort 100 names a minimum of 100 log(100) = 600 comparisons are needed. This takes 100 x 600/9000 = 6.7 sec. 45) The number of binary trees with 3 nodes which when traversed in post order gives the sequence A,B,C is? a. 3 b. 9 c. 7 d. 5 Explanation: Five trees are 46) The average search time of hashing with linear probing will be less if the load factor? a. is far less than one b. equals one c. is far greater than one d. none of above Explanation:Load factor is the ratio number of records that are currently present and the total number of records that can be present. If the load factor is less, free space will be more. This means probability of collision is less. So the search time will be less.

14 47) A binary tree that has n leaf nodes. The number of nodes of degree 2 in this tree is? a. log2n b. n - 1 c. n d. 2n Explanation: It can be proved by induction that a binary tree with n leaf nodes will have total of 2n - 1 nodes. So number of non-leaf nodes is (2n - 1)-n=n-1 48) The principal of locality justifies the use of? a. Interrupts b. DMA c. Polling d. Cache memory Explanation:In principal of phenomenon the same value or same memory location is being used frequently. 49) Sparse matrices have? a. many zero entries b. many non- zero entries c. higher dimension d. none of above Explanation: A sparse matrix is a matrix populated primarily with zeros 50) The postfix expression for * + a b - c d is? a. ab + cd - *

15 b. ab cd + - * c. ab + cd * - d. ab + - cd * 51) Hasse diagrams are drawn for a. partial ordered set. b. lattice c. boolean algebra d. none of these. Answer= A 52) A self complemented, distributive lattice is called a. Boolean algebra b. modular lattice. c. complete lattice Answer=A 53) Different partially ordered sets may be represented by the same hasse diagram if they are same. a. same b. lattice with same order c. isomorphic d. order isomorphic Answer=D 54)Total number of set of a set having four elements is

16 a. 16 b. 8 c. 15 d. 4 Answer=C 55) If * is defined on R* as a*b= ab/2, then identity element in the group (R*,*) is a. 1 b. 2 c. ½ d. 1/3 Answer =B 56) If sets A and B have 3 and 6 elements each, then minimum number of elements in AU B is a. 3 b. 6 c. 9 d. 18 Answer= B 57) order of the power set of a set of order n is a. n b. 2n c. n2 d. 2 n Answer=D

17 58) if F(x) and g(x) are defined on domains A,B respectively then domain of f(x)+g(x) is a. AUB b. A intersection B c). none of these d A-B Answer= B 59) Number of proper subsets of a set of ordered three is a. 3 b. 6 c. 8 d. 9 Answer=C 60)The number of distinct relation on a set of three element is a. 8 b. 9 c. 18 d. 512 Answer=D