UPKAR PRAKASHAN, AGRA-2

ByDr. Parashar & Prof. Arora

© Publishers

Publishers

UPKAR PRAKASHAN2/11A, Swadeshi Bima Nagar, AGRA–282 002Phone : 4053333, 2530966, 2531101Fax : (0562) 4053330E-mail : care@upkar.in, Website : www.upkar.in

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Price : 199·00 Only(Rs. One Hundred Ninety Nine Only)

Code No. 1940

Printed at : Upkar Prakashan (Printing Unit) Bye-pass, Agra

CONTENTS

1. Discrete Structures …………….……………………………………… 3–31

2. Computer Arithmetics ………………………………………………… 32–67

3. Principles of Programming in C & C++ ….…………………………… 69–113

4. Computer Graphics ………………………………....………………… 114–120

5. Concepts of Database Design and SQL ……………………………… 121–140

6. Data and File Structure ………………………………..……………… 141–157

7. Computer Networks and Transmission System ………….…………… 159–181

8. System Software and Compilers ……………………...……………… 182–201

9. Operating System …………………………………...………………… 202–238

10. Concepts of Software Engineering………………….....……………… 239–256

11. Current Trends and Technologies……………………………………… 257–272

12. Computer Hardware ………………………………………….……… 1–16

GENERAL INFORMATION

● REQUIRED QUALIFICATIONSThe Applicant must possess required qualification for the Contractual ICT posts (IT SupportingStaff) on the last date of submission of the on-line application form :

PostCode

Post Name Qualification

04 Contractual ICTPosts ( IT SupportingStaff)

Candidates should have Working knowledge of UNIX/OpenSource Software/Windows NT/Oracle and other RDMSpackages/programming languages with the followingminimum educational qualification—

(a). B.E. (Computer Science or related subject) or equivalenthigher qualification from a recognized University/Institution. OR

(b). M.C.A. /M.Sc. (Computer Science or related subject)from recognized University/Institution. OR

(c) Second Class Bachelors Degree from a recognizedUniversity with 'B' level course certificate from DOEACC/NIELIT.

● AGE(1) Every candidate for appointment by direct recruitment must have attained the minimum age

of 21 years and must not have crossed the age of 30 years as on stipulated date.

(2) Relaxation in Maximum age limit applicable to a candidate of Scheduled Castes andScheduled Tribes, and other reserved categories shall be as per the Government Orders,issued in this behalf, as adopted by the High Court.

● SYLLABUSKnowledge of UNIX/Open Source Software/Windows NT/Oracle and other RDMSpackages/programming languages.

● SELECTION PROCEDUREAll the Technical Manpower shall be selected through an open test to be conducted at two stages :

Stage 1 :Objective Test of 100 marks to test knowledge of computers including Software,Hardware and Networking consisting of 100 question and examination duration shall beof 90 minutes. The Test shall be conducted by an agency to be selected by the HighCourt after advertisement. There will be no negative marking.

Stage 2 : Practical Test of 25 marks—Candidates' practical knowledge of Programming will betested. Four times the number of Technical Manpower shortlisted at Stage 01 shall becalled for the Practical Test (Stage-02).

Preparation of Merit List of Selected Candidates—The merit list shall be prepared on the basisof marks obtained by the candidates in Objective Test (Stage-1) and Practical Test (Stage-2). In theevent candidates obtain the same number of marks, the candidates born earlier shall be placedhigher in Merit. Candidates will have to clear both the Stage-I and Stage-II Tests.

ObjectiveComputer Science

Discrete Structures1. Context free grammar is—

(A) A compiler(B) A language generator(C) A regular expression(D) None of these

2. The idea of an automation with a stack asauxiliary storage—(A) Finite automata(B) Pushdown automata(C) Deterministic automata(D) None of the above

3. A Pushdown automata is ……… if there is atmost one transition applicable to each con-figuration.(A) Deterministic (B) Non-deterministic(C) Finite (D) Non-finite

4. The graphical representation of the transitionof finite automata is—(A) Finite diagram (B) State diagram(C) Node diagram (D) E-R diagram

5. If two sets A and B have no commonelements, i.e., A ∩ B has no elements, suchsets are known as—(A) Intersection (B) Union(C) Disjoint (D) Complement

6. The domain D of the relation R is defined asthe—(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(D) None of the above

7. ‘A language is regular if and only if it isaccepted by a finite automation’—(A) The given statement is true(B) The given statement is false(C) The given statement is partially true(D) Sometimes true, sometimes false

8. Which of the following does not belong to thecontext free grammar?(A) Terminal symbol(B) Non-terminal symbol(C) Start symbol(D) End symbol

9. A regular grammar is a—(A) Context free grammar(B) Non-context free grammar(C) English grammar(D) None of the above

10. The context free languages are closed under—(A) Union (B) Kleene star(C) Concatenation (D) All of these

11. A graph is a collection of—(A) Row and columns(B) Vertices and edges(C) Equations(D) None of these

12. The degree of any vertex of graph is—(A) The number of edges incident with the

vertex(B) Number of vertex in a graph(C) Number of vertices adjacent to that

vertex(D) Number of edges in a graph

13. If for some positive integer k , degree ofvertex d (v) = k for every vertex v of the graphG, then G is called—(A) K graph (B) K-regular graph(C) Empty graph (D) All of these

14. A graph with no edges is called as emptygraph. Empty graph also known as—(A) Trivial graphs (B) Regular graphs(C) Bipartite graphs (D) None of these

15. Length of the walk of a graph is—(A) The number of vertices in walk W(B) The number of edges in walk W

4A | Computer Science

(C) Total number of edges in a graph(D) Total number of vertices in a graph

16. If the origin and terminus of a walk are same,the walk is known as—(A) Open (B) Closed(C) Path (D) None of these

17. A graph G is called a ……. if it is a connectedacyclic graph.(A) Cyclic graph (B) Regular graph(C) Tree (D) Not a graph

18. Eccentricity of a vertex denoted by e(v) isdefined by—(A) max {d(u, v): u ∈ v, u ≠ v}

(where d (u, v) is the distance of vertex uand vertex v).(B) min {d(u, v): u ∈ v, u ≠ v}(C) Both (A) and (B)(D) None of these

19. Radius of a graph, denoted by rad (G) isdefined by—(A) min {e(v) : v ∈ V}

(where e(v) is eccentricity of vertex, v isa vertex and V is the vertex set)(B) max {e(v): v ∈ V}(C) max {d(u, v): U ∈ V, U ≠ V}(D) min {d(u, v): U ∈ V, U ≠ V}

20. The complete graph Kn has ……… differentspanning trees.(A) nn – 2 (B) n × n(C) nn (D) n2

21. A tour of G is a closed walk of graph G whichincludes every edge of G atleast once. A……… tour of G is a tour which includesevery edge of G exactly once.(A) Hamiltonian (B) Planar(C) Isomorphic (D) Euler

22. Which of the following is not a type of graph?(A) Euler (B) Hamiltonian(C) Tree (D) Path

23. Choose the most appropriate definition ofplane graph—(A) A graph drawn in a plane in such a way

that any pair of edges meet only at theirend vertices

(B) A graph drawn in a plane in such a waythat if the vertex set of graph can bepartitioned into two non-empty disjointsubsets X and Y in such a way that eachedge of G has one end in X and one endin Y

(C) A simple graph which is isomorphic to aHamiltonian graph

(D) None of the above

24. Match the following—List-I(a) Tree (b) Centrer of graph(c) Walk (d) Trivial Graph

List-II

(i) No edges(ii) Set of all central points(iii) No cycle(iv) Finite sequence(v) Set of all degrees

Codes :

(a) (b) (c) (d)(A) (iv) (v) (i) (ii)(B) (iii) (ii) (iv) (i)(C) (iii) (ii) (iv) (v)(D) (v) (iv) (iii) (ii)

25. A continuous non-intersecting curve in theplane whose origin and terminus coincide?(A) Planar (B) Jordan(C) Hamiltonian (D) All of these

26. 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 the above

27. A path in graph G, which contains everyvertex of G once and only once ?(A) Eulartour (B) Hamiltonian path(C) Eular trail (D) Hamiltonian tour

28. A minimal spanning tree of a graph G is—(A) A spanning subgraph(B) A tree(C) Minimum weights(D) All of the above

Computer Science | 5A

29. A tree having a main node, which has nopredecessor is—(A) Spanning tree (B) Rooted tree(C) Weighted tree (D) None of these

30. Diameter of a graph denoted by diam (G) isdefined by—(A) max {e (v) : v ∈ V}

(where e (v) is eccentricity of vertex, vis a vertex and V is the vertex set)

(B) max {d (u, v): u, v ∈ V}(where d (u, v) is the distance betweentwo vertices U and V)

(C) Both (A) and (B)(D) None of these

31. A vertex of a graph is called odd or evendepending on whether—(A) Total number of edges in graph is odd or

even(B) Total number of vertices in graph is odd

or even(C) Its degree is odd or even(D) None of these

32. All the vertices of a walk except very first andvery last vertex, is called—(A) Internal vertices(B) External vertices(C) Intermediate vertices(D) Adjacent vertices

33. Let A be a finite set of size n. The number ofelements in the power set of A × A is—

(A) 22n

(B) 2n2

(C) (2n)2 (D) (22)n

34. The less-than relation "<" on real number is—(A) A partial ordering since it is symmetric

and reflexive(B) A partial ordering since it is anti-

symmetric and reflexive(C) Not a partial ordering because it not

asymmetric and not reflexive(D) Not a partial ordering because it is not

antisymmetric and not reflexive35. Let X and Y be sets with cardinalities m and n

respectively. The number of one-one mappingfrom X to Y when m < n is—(A) mn (B) npm

(C) mCn (D) nCm

36. Let A and B be any two arbitrary events thenwhich one of the following is true ?(A) P(A ∩ B) = P(A) . P(B)(B) P(A ∪ B) = P(A) + P(B)(C) P(A|B) = P(A ∩ B) . P(B)(D) P(A ∪ B) ≤ P(A) + P(B)

37. Probability that two randomly selected cardsfrom a set of two red and two black cards, areof the same colour is—

(A)12

(B)13

(C)23

(D) None of these

38. The number of sub strings (of all lengthsinclusive) that can be formed from a Characterstring of length n is—(A) n (B) n2

(C)n (n – 1)

2(D)

n (n + 1)2

39. In a tree between every pair of vertices thereis—(A) n number of paths(B) Exactly one path(C) A self loop(D) Two circuits

40. Suppose R be non-empty relation on acollection of sets defined by ARB if and onlyif A ∩ B=Ø. Then—(A) R is reflexive and transitive(B) R is an equivalence relation(C) R is symmetric and not transitive(D) R is not reflexive and not transitive

41. Let P and Q be sets and P and Q denote thecomplements of sets P and Q. The set (P-Q)U (P-Q) U (P ∩ Q) is equal to—(A) P ∪ Q (B) Pc ∪ Cc

(C) P ∩ Q (D) Pc ∩ Qc

42. Let S be an infinite set and S1, S2, S3, ... Sn besets such that S1 ∪ S2 ∪ S3 ∪ S4 ∪……….Sn

= S. Then—(A) At least one of the sets Si is a finite set

(B) At least one of the sets Si is an infiniteset

6A | Computer Science

(C) Not more than one of the set Si can befinite

(D) None of the above

43. Suppose A is a finite set f with n elements.The number of elements in the largest equi-valence relation of A is—(A) n (B) n2

(C) 1 (D) n + 1

44. The relation R = {(x, y) ∈ N × N | x1 y} is—(A) Reflexive (B) Symmetric(C) Antisymmetric (D) Transitive

45. The number of subset of {1, 2, ..........n} withodd cardinality is—(A) 2n (B) n2

(C) 2n–1 (D) 22n

46. The power set 2s of the set S = {3, {1, 4}, 5}is—(A) {S,3,{1,4},5}(B) {S},3,1,4,{1,3,5},{1,4,5},{3,4},Ø}(C) {S,{3},{3,{1,4}},{3,5},Ø}(D) None of the above

47. If P(S) denotes the power set of set S, thenwhich of the following is always true ?(A) P(S) ∩ P (P(S)) = {Ø}(B) P (P(S)) =P(S)(C) P(S) ∩ S =P(S)(D) S � P(S)

48. Transitive and irreflexive imply—(A) Symmetric (B) Reflexive(C) Irreflexive (D) Asymmetric

49. Pigenhole principle states that if A → B and|A| > |B| then—(A) f is not onto(B) f is not one-one(C) f is neither one-one nor onto(D) f may be one-one

50. Which of the following are posets—(A) (Z, =) (B) (Z, 1)(C) (Z, X) (D) (Z, X)(Z is the set of integers).

51. A graph is planar if and only if—(A) It does not contain subgraph homomor-

phic to K5 and K3, 3

(B) It does not contain subgraph isomorphicto K5 and K3, 3

(C) It contains subgraph homomorphic to K5

and K3, 3

(D) It contains subgraph isomorphic to K5

and K3, 3

52. If G is an undirected planar graph on nvertices with e edges then—(A) e ≤ n (B) e ≤ 2n(C) e ≤ 3n (D) None of these

53. In an undirected graph, the number of nodeswith odd degree must be—(A) Zero (B) Even(C) Odd (D) Prime

54. A binary tree T has n leaf nodes. The numberof nodes of degree 2 in T is—(A) log n (B) n – 1(C) 2n (D) 2n

55. The minimum number of edges in a con-nected cyclic graph on n vertices is—(A) n – 1 (B) n(C) n + 1 (D) None of these

56. Let G be a graph with 100 vertices numbered1 to 100. Two vertices i and j are adjacent if|i – j | = 8 or |i – j| = 12. The number ofconnected components in G is—(A) 8 (B) 4(C) 12 (D) 25

57. What is the total number of edges in thecomplete graph on n vertices?(A) n (B) nc2

(C) nnc2 (D)n (n – 1)

2

58. Which of the following statement is false?(A) A tree with n nodes has n – 1 edges(B) A labeled rooted binary tree can be

uniquely constructed given its post orderand preorder traversal result

(C) A complete binary tree with n internalnodes has (n + 1) leaves

(D) The maximum number of nodes in abinary tree of height h is 2h + i – 1

59. Consider the following statements—S1: There exist infinite sets A, B and C suchthat A (B·C) is finite.

Computer Science | 7A

S2: There exist two irrational number x and ysuch that (x + y) is rational.Which of the following is true about S1 andS2?(A) Only S1 is correct(B) Only S2 is correct(C) Both S1 and S2 are correct(D) None of the above

60. The binary relation S=Ø (empty set) on setA = {1, 2, 3} is—(A) Transitive and reflexive(B) Transitive and symmetric(C) Symmetric and reflexive(D) Neither reflexive nor symmetric

61. How many pendant vertices are there in anytree?(A) One (B) None(C) At least one (D) At least two

62. Which of the following statement is false?(A) The complete graph of five vertices is

planar(B) Kuratowski's second graph is non planar(C) A graph in which all vertices are of equal

degree is a regular graph(D) The distance between vertices of a

connected graph is a metric63. What is the maximum number of the edges

can a simple graph with n vertices and kcomponents have?(A) n – k(B) (n – k) (n – k + 1)(C) (n – k) (n – k + 1)/2(D) (n + k + 1)

64. A given connected graph G is an Euler graphif—(A) All vertices of G are of even degree(B) All vertices of G are of odd degree(C) All vertices of G are equal(D) It cannot be decomposed into circuits

65. Which of the following statement is true?(A) Every graph is not its own sub graph(B) A single vertex in a graph G is a sub

graph of G(C) The terminal vertices of a path are of

degree two(D) A tree with n vertices has n edges

66. The number of edges in a regular graph ofdegree d and n vertices is—(A) n + d (B) nd(C) n d/2 (D) nd

67. The number of circuit that can be created byadding an edge between any two vertices in atree is—(A) Two (B) Exactly one(C) At least one (D) None

68. A non planar graph with minimum number ofvertices has—(A) 9 edges, 6 vertices(B) 6 edges, 4 vertices(C) 10 edges, 5 vertices(D) 9 edges, 5 vertices

69. The graph of Königsberg bridges is not anEular graph because—(A) It has 4 vertices and 7 edges(B) Not all its vertices are of even degree(C) It does not have a self loop(D) It is not connected

70. In a tree, between every pair of vertices thereis—(A) Exactly one path (B) A self loop(C) Two circuit (D) n number of path

71. Suppose A is a finite set with n elements. Thenumber of elements in the largest equivalencerelation of A is—(A) n (B) n2

(C) n + 1 (D) 1

72. Which of the following sets can be recog-nized by a Deterministic Finite-state Automa-tion?(A) The numbers 1, 2, 4, 8, ...., 2n, .... written

in binary(B) The set of binary strings in which the

number of zeros is the same as thenumber of ones

(C) The numbers 1, 2, 4, ...., 2n, .... written inunary

(D) The set {1, 101, 11011, 1110111, ….}

73. The string 1101 does not belong to the setrepresented by—(A) 110* (0 + 1)(B) (10)* (01)* (00 + 11)*(C) 1 (0 + 1)* 101(D) (00 + (11)* 0)*

8A | Computer Science

74. The number of elements in the power set P(S)of the set S= {{Ø}, 1, {2, 3}} is—(A) 2 (B) 4(C) 8 (D) 10

75. Regarding the power of recognition of langu-ages, which of the following statement isfalse?(A) The non-deterministic Finite-State au-

tomata are equivalent to deterministicFinite-State automata

(B) Non-deterministic Turing machines areequivalent to deterministic Turingmachines

(C) Non-deterministic Pushdown automataare equivalent to deterministic Push-down automata

(D) Multi-tape Turing machines are equiva-lent to Single-tape Turing machines

76. The number of binary relations on a set with nelements is—

(A) n2 (B) 2n

(C) 2n2 (D) None of these

77. Let A is a finite set with n elements. Thenumber of elements in the largest equivalencerelation of A is—(A) n2 (B) n(C) n + 1 (D) 1

78. Which of the following statements is false?(A) Every subset of a regular set is regular(B) Every finite subject of a non-regular set

is regular(C) Every finite subset of a regular set is

regular(D) The intersection of two regular sets is

regular

79. In a room containing 28 people, there are 18people who speak English, 15 people whospeak Hindi and 22 people who speakKannada. 9 persons speak both English andHindi, 11 persons speak both Hindi andKannada whereas 13 persons speak bothKannada and English. How many peoplespeak all the three languages?(A) 7 (B) 9(C) 8 (D) 6

80. The number of equivalence relations of theset {1, 2, 3, 4} is—(A) 15 (B) 16(C) 24 (D) 4

81. Two girls have picked 10 roses, 15 sun-flowers and 14 daffodils. What is the numberof ways they can divide the flowers amongstthemselves?(A) 1,638 (B) 2,640(C) 2,100 (D) None of these

82. Consider the regular expression (0 + 1) (0 + 1).... n times. The minimum state finite auto-mation that recognizes the language repre-sented by this regular expression contains.(A) n states (B) n + 2 states(C) n + 1 states (D) None of these

83. Context-free languages are closed under—(A) Union, intersection(B) Intersection, complement(C) Union, Kleene closure(D) Complement, Kleene Closure

84. A continuous non–intersecting curve in theplane whose origin and terminus coincide is—(A) Hamiltonian (B) Planer(C) Jordan (D) All of these

85. The number of functions from an m elementset to an n element set is—(A) m + n (D) m*n

(C) mn (D) nm

86. In a room containing 28 females, there are 18females who speak English, 15 females speakHindi and 22 speak Punjabi. 9 females speakboth English and Hindi, 11 females speakboth Hindi and Punjabi whereas 13 speakboth Punjabi and English. How many femalesspeak all the three languages?(A) 6 (B) 7(C) 8 (D) 9

87. The minimum number of cards to be dealtfrom an arbitrarily shuffled deck of 52 cardsto guarantee that three cards are from somesame suit is—(A) 8 (B) 3(C) 9 (D) 12

Computer Science | 9A

88. Let S and T be languages over Σ = {a, b}represented by the regular expressions (a +b*)* and (a + b)*, respectively. Which of thefollowing is true?(A) S ⊂ T (B) S ∩ T = 0(C) S = T (D) T ⊂ S

89. If L1 is a context-free language and L2 is aregular language, which of the followingis/are false?(A) L1 – L2 is not context free(B) ~L1 is context free(C) L1 ∩ L2 is context free(D) ~L2 is regular

90. Let L be a set with a relation R which istransitive, antisymmetric and reflexive and forany two elements a, b ∈ L let the least upperbound lub (a, b) and the greatest lower boundglb (a, b) exist. Which of the following is/aretrue?(A) L is poset(B) L is a lattice(C) L is a boolean algebra(D) None of the above

91. E1 and E2 are events in a probability spacesatisfying the following constraints :Pr(E1) = Pr(E2)Pr(E1 ∪ E2) = 1E1 and E2 are independent.The value of Pr(E1), the probability of theevent E1, is—

(A) 0 (B) 1/2(C) 1/4 (D) 1

92. A relation r is defined on the set of integers asxRy if (x + y) is even. Which of the followingstatements is true?(A) R is not an equivalence relation(B) R is an equivalence relation having 1

equivalence class(C) R is an equivalence relation having 2

equivalence classes(D) R is an equivalence relation having 3

equivalence classes

93. Each of the function 2ln and nlog n has growthrate ………… that of any polynomial.(A) equal to (B) greater than(C) less than (D) proportional to

94. Suppose A and B be sets with cardinalities mand n respectively. The number of one-to-onemapping from A to B where m < n is—(A) mn (B) nPm

(C) mCn (D) nCm

95. Suppose A be set of integer greater than 1 andsmaller than 1000. Let b denote set of booksin library, |B| = 999. Let f : A → B, assigninga unique number to each book is—(A) one to one , onto(B) one to one ,and not onto(C) not one to one ,onto(D) not one to one, not onto

96. Which of the following is an unordered col-lection of elements where an element canoccur as a member more than once?(A) Set (B) Multiset(C) Ordered set (D) None of these

97. The probability that a number selected atrandom between 100 and 999 (both inclusive)will not contain the digit 7 is—(A) 16/25 (B) 27/75(C) (9/10)3 (D) 18/25

98. The number of substrings of all lengths thatcan be formed from a character string oflength is equal to—

(A) n (B) n2

(C) n(n + 1)/2 (D) n(n – 1)/2

99. The number of elements in the power set P(S)of the set S = {{φ}, 1, {2, 3}} is—(A) 4 (B) 2(C) 8 (D) None of these

100. If G is an undirected planer graph on nvertices with e edges then ? (A) e < = n (B) e < = 2n(C) e < = 3n (D) None of these

101. A bag contains 10 white balls and 15 blackballs. Two balls are drawn in succession. Theprobability that one of them is black and theother is white is—(A) 4/5 (B) 2/3(C) 1/2 (D) 1/3

10A | Computer Science

102. Which of the following is not a type of graph ?(A) Euler (B) Hamiltonian(C) Path (D) Tree

103. Let a and b are sets and |a| and |b| are theirrespective cardinalities. It is given that thereare exactly 97 functions from x to y . Fromthis one can conclude that—(A) |a| = 1, |b| = 97 (B) |a| = 97, |b| = 1(C) |a| = 97, |b| = 97 (D) None of these

104. In the lattice defined by the Hasse diagramgiven in Fig., how many complements doesthe element ‘e’ have?

(A) 2 (B) 3(C) 1 (D) 0

105. The probability that it will rain today is 0.5.The probability that it will rain tomorrow is0.6. The probability that it will rain eithertoday or tomorrow is 0.7. What is the proba-bility that will rain today and tomorrow?(A) 0.3 (B) 0.35(C) 0.25 (D) 0.4

106. Given Σ = {a, b}, which one of the followingsets is not countable?(A) Set of all regular languages over Σ(B) Set of all languages over Σ(C) Set of all strings over Σ(D) Set of all languages over Σ accepted by

Turing machines

107. The number of equivalence relations on theset {1, 2, 3, 4} is—(A) 16 (B) 15(C) 24 (D) 4

108. Which one of the following regular expres-sions over {0, 1} denotes the set of all stringsnot containing 100 as a substring?(A) 0* (1 + 0)* (B) 0* (10 + 1)*(C) 0* 1010* (D) 0* 1* 01*

109. A partial order ≤ is defined on the set S = {x,a1, a2, ...., an, y) as x ≤ ai for all i and ai ≤ yfor all i, where n ≥ 1. The number of totalorders on the set S which contain the partialorder ≤ is—(A) n ! (B) n(C) n + 2 (D) 1

110. Let G be a graph with 100 vertices numbered1 to 100. Two vertices i and j are adjacent if|i – j| = 8 or |i –j| = 12. The number ofconnected components in G is—(A) 8 (B) 4(C) 25 (D) 12

111. Which one of the following is not decidable?(A) Equivalence of two given Turing mach-

ines(B) Language accepted by a given finite state

machine is non-empty(C) Given a turing machine M, a string s and

an integer k, M accepts s within k steps(D) Language generated by a context-free

grammar is non-empty112. Which one of the following is the most

appropriate definition of plane graph? (A) A simple graph which is isomorphic to

Hamiltonian graph(B) A graph drawn in a plane in such a way

that any pair of edges meet only at theirend vertices

(C) A graph drawn in a plane in such a waythat if the vertex set of graph can bepartitioned into two non-empty disjointsubset X and Y in such a way that eachedge of G has one end in X and one endin Y

(D) None of these113. A path in graph G, which contains every

vertex of G once and only once is called—(A) Eular tour(B) Eular trail(C) Hamiltonian Path(D) Hamiltonian tour

114. A die is rolled three times. The probabilitythat exactly one odd number turns up amongthe outcomes is—(A) 1/6 (B) 3/8(C) 1/2 (D) 1/8

Computer Science | 11A

115. Consider the function y = | x | in the interval[– 1, 1]. In this interval, the function is—(A) continuous and differentiate(B) differentiable but not continuous(C) continuous but not differentiable(D) neither continuous nor differentiable

116. Which of the following statements applies tothe bisection method used for finding roots offunctions?(A) is faster than the Newton-Raphson

method(B) guaranteed to work for all continuous

functions(C) converges within a few iterations(D) requires that there be no error in deter-

mining the sign of the function117. A tree having a main node, which has no

predecessor is a—(A) Rooted tree (B) Spanning tree(C) Weighted tree (D) None of these

118. What is the converse of the followingassertion?I stay only if you go(A) I stay if you go(B) If you do not go then I do not stay(C) If I stay then you go(D) If I do not stay then you go

119. The number of functions from an m elementset to an n element is—(A) mn (B) m + n(C) nm (D) m * n

120. Let R1 and R2 be two equivalence relations ona set. Consider the following assertions—(i) R1 ∪ R2 is an equivalence relation(ii) R1 ∩ R2 is an equivalence relationWhich of the following is correct ?(A) Both assertions are true(B) Assertion (i) is true but assertion (ii) is

not true(C) Assertion (ii) is true but assertion (i) is

not true(D) Neither (i) nor (ii) is true

121. Let P(S) denote the power set of set S. Whichof the following is always true?(A) P(P (S)) = P(S)(B) P(S) ∩ S = P(S)

(C) P(S) ∩ P(P(S)) = {φ}(D) S ∈ P(S)

122. What can be said about a regular language L,over {a} whose minimal finite state automa-tion has two states?(A) L must be {an / n is even}(B) L must be {an / n is odd}(C) I must be {an / n ≥ 0}(D) Either L must be {an/n is odd},or L must

be {an/n is even}123. A vertex of a graph is called even or odd

depending upon—(A) Its degree is even or odd(B) Total number of edges in a graph is even

or odd(C) Total number of vertices in a graph is

even or odd(D) All of the above

124. The collection of all subset of a set A is itselfa set, called the—(A) Proper set (B) Power set(C) Elementary set (D) Empty set

125. A null set is denoted by— (A) ( ) (B) φ

(C) — (D) None of these

126. If set A = {4, 5, 6, 7, 8, 9} and set B = {3, 5,2, 7} then A – B is—(A) {3, 2} (B) {4, 6, 8, 9}(C) {6, 7, 8, 9} (D) None of these

127. The symmetric difference of set A and B isdenoted by—(A) A – B (B) A Δ B(C) A θ B (D) A – A

128. The …….. of two sets A and B is the set ofall those pairs whose first coordinate is anelement of A and the second coordinate is anelement of B. The set is denoted by A × B.(A) Graph (B) Cartesian product(C) Product (D) Superset

129. Let A = {1, 2, 3}, B = {a, b) and R = {(1, a),(1, b), (3, a), (2, b)} be a relation from A to B.The inverse relation R is—(A) R–1 = {(a, 1), (b, 1), (a, 3), (b, 2)}(B) R–1 = {(2, b), (3, a), (1, b), (1, a)}

Allahabad High Court Contractual ICTPosts (IT Supporting Staff) Recruitment

Exam.

Publisher : Upkar PrakashanAuthor : Dr. Prashar & Prof.Arora

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