A tree with n vertices is called graceful, if its vertices can be labelled with integers 1, 2, ...,n such that the absolute value of the difference of the labels of adjacent vertices are all different. Which of the following trees are graceful?

A tree with n vertices is called graceful, if its vertices can be labelled with integers 1, 2, ...,n such that the absolute value of the difference of the labels of adjacent vertices are all different. Which of the following trees are graceful?

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Codes: (A) (a) and (b) (B) (b) and (c) (C) (a) and (c) (D) (a), (b) and (c)

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Answer :

Answer: D

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Related questions

Consider the following statements: (a) Depth - first search is used to traverse a rooted tree. (b) Pre - order, Post-order and Inorder are used to list the vertices of an ordered rooted tree. (c) Huffman's algorithm is used to find an optimal binary tree with given weights. (d) Topological sorting provides a labelling such that the parents have larger labels than their children. Which of the above statements are true ? (A) (a) and (b) (B) (c) and (d) (C) (a) , (b) and (c) (D) (a), (b) , (c) and (d)

Description : Consider the following statements: (a) Depth - first search is used to traverse a rooted tree. (b) Pre - order, Post-order and Inorder are used to list the vertices of an ordered rooted tree. (c) Huffman's algorithm is used to find an optimal ... (d) (C) (a) , (b) and (c) (D) (a), (b) , (c) and (d)

Last Answer : (D) (a), (b) , (c) and (d)

A certain tree has two vertices of degree 4, one vertex of degree 3 and one vertex of degree 2. If the other vertices have degree 1, how many vertices are there in the graph? (A) 5 (B) n – 3 (C) 20 (D) 11

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Last Answer : (D) 11

If n and r are non-negative integers and n≥r, then p(n + 1, r) equals to (A) P(n,r)(n+1) / (n+1-r) (B) P(n,r)(n+1) / (n-1+r) (C) p(n,r)(n-1) / (n+1-r) (D) p(n,r)(n+1) / (n+1+r)

Description : If n and r are non-negative integers and n≥r, then p(n + 1, r) equals to (A) P(n,r)(n+1) / (n+1-r) (B) P(n,r)(n+1) / (n-1+r) (C) p(n,r)(n-1) / (n+1-r) (D) p(n,r)(n+1) / (n+1+r)

Last Answer : (A) P(n,r)(n+1) / (n+1-r)  Explanation: p(n, r) = n!/(n-r)! p( n+1, r) = (n+1)!/(n+1-r)! = (n+1) n! /(n+1-r) (n-r)! = P(n, r)(n+1)/(n+1-r)

Which of the following algorithms sort n integers, having the range 0 to (n2 -1), in ascending order in O(n) time ? (A) Selection sort (B) Bubble sort (C) Radix sort (D) Insertion sort

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Last Answer : (C) Radix sort

If there are n integers to sort, each integer has d digits and each digit is in the set {1,2, ..., k}, radix sort can sort the numbers in: (A) O(d n k) (B) O(d nk) (C) O((d+n)k) (D) O(d(n+k))

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Last Answer : (D) O(d(n+k))

Let P(m,n) be the statement “m divides n” where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions. (a) ∃m ∀n P(m,n) (b) ∀n P(1,n) (c) ∀m ∀n P(m,n) (A) (a)-True; (b)-True; (c)-False (B) (a)-True; (b)-False; (c)-False (C) (a)-False; (b)-False; (c)-False (D) (a)-True; (b)-True; (c)-True

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Last Answer : Answer: A

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Last Answer : (C) M-N+C

Cyclometric complexity of a flow graph G with n vertices and e edges is (A) V(G) = e+n-2 (B) V(G) = e-n+2 (C) V(G) = e+n+2 (D) V(G) = e-n-2

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Last Answer : (B) V(G) = e-n+2

A graph is said to be ……………… if the vertices can be split into two sets V1 and V2 such there are no edges between two vertices of V1 or two vertices of V2. A) Partite B) Bipartite C) Rooted D) Bisects

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Last Answer : B) Bipartite

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Last Answer : (C) If (u, v) ∈ E then u ∈ V1 or v ∈ V1

Compute the value of adding the following two fuzzy integers: A = {(0.3,1), (0.6,2), (1,3), (0.7,4), (0.2,5)} B = {(0.5,11), (1,12), (0.5,13)} Where fuzzy addition is defined as μA+B(z) = maxx+y=z (min(μA(x), μB(x))) Then, f(A+B) is equal to (A) {(0.5,12), (0.6,13), (1,14), (0.7,15), (0.7,16), (1,17), (1,18)} (B) {(0.5,12), (0.6,13), (1,14), (1,15), (1,16), (1,17), (1,18)} (C) {(0.3,12), (0.5,13), (0.5,14), (1,15), (0.7,16), (0.5,17), (0.2,18)} (D) {(0.3,12), (0.5,13), (0.6,14), (1,15), (0.7,16), (0.5,17), (0.2,18)}

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Last Answer : (2) O(log n) 

A graph is a collection of nodes, called ………. And line segments called arcs or ……….. that connect pair of nodes. A) vertices, edges B) edges, vertices C) vertices, paths D) graph node, edges

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Last Answer : A) vertices, edges

State True or False. i) An undirected graph which contains no cycles is called forest. ii) A graph is said to be complete if there is an edge between every pair of vertices. A) True, True B) False, True C) False, False D) True, False

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Last Answer : A) True, True

State True of False. i) Network is a graph that has weights or costs associated with it. ii) An undirected graph which contains no cycles is called a forest. iii) A graph is said to be complete if there is no edge between every pair of vertices. A) True, False, True B) True, True, False C) True, True, True D) False, True, True

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A structure brings together a group of A) items of the same data type B) related data items and variables C) integers with user defined names D) floating points with user defined names

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Last Answer : B) related data items and variables

The relation "divides" on a set of positive integers is .................. (A) Symmetric and transitive (B) Anti symmetric and transitive (C) Symmetric only (D) Transitive only

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Last Answer : (B) Anti symmetric and transitive Explanation: The ‘divide’ operation is antisymmetric because if a divides b does not necessarily implies that b divides a. If a divides b and b divides c then a divides c. So, it is transitive as well.

Let f and g be the functions from the set of integers to the set integers defined by f(x) = 2x + 3 and g(x) = 3x + 2 Then the composition of f and g and g and f is given as (A) 6x + 7, 6x + 11 (B) 6x + 11, 6x + 7 (C) 5x + 5, 5x + 5 (D) None of the above

Description : Let f and g be the functions from the set of integers to the set integers defined by f(x) = 2x + 3 and g(x) = 3x + 2 Then the composition of f and g and g and f is given as (A) 6x + 7, 6x + 11 (B) 6x + 11, 6x + 7 (C) 5x + 5, 5x + 5 (D) None of the above

Last Answer : (A) 6x + 7, 6x + 11 Explanation: fog(x)=f(g(x))=f(3x+2)=2(3x+2)+3=6x+7 gof(x)=g(f(x))=g(2x+3)=3(2x+3)+2=6x+11

What does the following declaration mean ? int (*ptr) [10]; (A) ptr is an array of pointers of 10 integers. (B) ptr is a pointer to an array of 10 integers. (C) ptr is an array of 10 integers. (D) none of the above.

Description : What does the following declaration mean ? int (*ptr) [10]; (A) ptr is an array of pointers of 10 integers. (B) ptr is a pointer to an array of 10 integers. (C) ptr is an array of 10 integers. (D) none of the above.

Last Answer : (B) ptr is a pointer to an array of 10 integers.

Let A and B be two fuzzy integers defined as: A={(1,0.3), (2,0.6), (3,1), (4,0.7), (5,0.2)} B={(10,0.5), (11,1), (12,0.5)} Using fuzzy arithmetic operation given by Image (A) {(11,0.8), (13,1), (15,1)} (B) {(11,0.3), (12,0.5), (13,1), (14,1), (15,1), (16,0.5), (17,0.2)} (C) {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,1), (16,0.5), (17,0.2)} (D) {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5), (17,0.2)}

Description : Let A and B be two fuzzy integers defined as: A={(1,0.3), (2,0.6), (3,1), (4,0.7), (5,0.2)} B={(10,0.5), (11,1), (12,0.5)} Using fuzzy arithmetic operation given by (A) {(11,0.8), (13,1), (15,1)} ( ... ,0.2)} (D) {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5), (17,0.2)}

Last Answer : (D) {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5), (17,0.2)}

Which of the following is/are not true? (a) The set of negative integers is countable. (b) The set of integers that are multiples of 7 is countable. (c) The set of even integers is countable. (d) The set of real numbers between 0 and 1/2 is countable. (A) (a) and (c) (B) (b) and (d) (C) (b) only (D) (d) only

Description : Which of the following is/are not true? (a) The set of negative integers is countable. (b) The set of integers that are multiples of 7 is countable. (c) The set of even integers is countable. (d) The set of real numbers between 0 ... . (A) (a) and (c) (B) (b) and (d) (C) (b) only (D) (d) only

Last Answer : (D) (d) only

Suppose you are given a binary tree with n nodes, such that each node has exactly either zero or two children. The maximum height of the tree will be (A) n/2 - 1 (B) n/2 + 1 (C) (n-1)/2 (D) (n+1)/2

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Last Answer : (C) (n-1)/2

A ................. complete subgraph and a ................. subset of vertices of a graph G=(V,E) are a clique and a vertex cover respectively. (A) minimal, maximal (B) minimal, minimal (C) maximal, maximal (D) maximal, minimal

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Last Answer : (D) maximal, minimal 

Consider the following statements : (a) Boolean expressions and logic networks correspond to labelled acyclic digraphs. (b) Optimal Boolean expressions may not correspond to simplest networks. (c) Choosing essential blocks first in a Karnaugh map and then greedily choosing the largest remaining blocks to cover may not give an optimal expression. Which of these statement(s) is/ are correct? (A) (a) only (B) (b) only (C) (a) and (b) (D) (a), (b) and (c)

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Last Answer : (D) (a), (b) and (c) 

Let ABCD be a parallellogram. Let m and n be positive integers such that n < m < 2n. Let AC = 2 mn -Maths 9th

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In the …………….. traversal we process all of a vertex’s descendents before we move to an adjacent vertex. A) Depth First B) Breadth First C) With First D) Depth Limited

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In a typical mobile phone system with hexagonal cells, it is forbidden to reuse a frequency band in adjacent cells. If 840 frequencies are available, how many can be used in a given cell? (A) 280 (B) 210 (C) 140 (D) 120

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Last Answer : Answer: A Explanation: Each cell has six other adjacent cells, in a hexagonal grid. If the central cell uses frequency group A, its six adjacent cells can use B, C, B, C, B, and C respectively. In other words, only 3 unique cells are needed. So the answer is 840/3 = 280 frequencies.

Consider a 3-puzzle where, like in the usual 8-puzzle game, a tile can only move to an adjacent empty space. Given the initial state which of the following state cannot be reached?

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Last Answer : Answer: C

................ is used in game trees to reduce the number of branches of the search tree to be traversed without affecting the solution. (A) Best first search (B) Goal stack planning (C) Alpha-beta pruning procedure (D) Min-max search

Description : ................ is used in game trees to reduce the number of branches of the search tree to be traversed without affecting the solution. (A) Best first search (B) Goal stack planning (C) Alpha-beta pruning procedure (D) Min-max search

Last Answer : (C) Alpha-beta pruning procedure

Shift-Reduce parsers perform the following : (A) Shift step that advances in the input stream by K(K>1) symbols and Reduce step that applies a completed grammar rule to some recent parse trees, joining them together as one tree with a new root symbol. (B) Shift step that advances in the input stream by one symbol and Reduce step that applies a completed grammar rule to some recent parse trees, joining them together as one tree with a new root symbol. (C) Shift step that advances in the input stream by K(K = 2) symbols and Reduce step that applies a completed grammar rule to form a single tree. (D) Shift step that does not advance in the input stream and Reduce step that applies a completed grammar rule to form a single tree.

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Last Answer : (B) Shift step that advances in the input stream by one symbol and Reduce step that applies a completed grammar rule to some recent parse trees, joining them together as one tree with a new root symbol.

An ordinal scale is: a. The simplest form of measurement b. A rank-order scale of measurement c. A scale with equal intervals between adjacent numbers d. A scale with an absolute zero point e. A categorical scale

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Which of the following arguments are not valid? (a) “If Gora gets the job and works hard, then he will be promoted. If Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard”. (b) “Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty”. (c) If n is a real number such that n>1, then n2>1. Suppose that n2>1, then n>1. Codes: (A) (a) and (c) (B) (b) and (c) (C) (a), (b) and (c) (D) (a) and (b)

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Last Answer : Answer: B Explanation: (a) P: Gora gets the job  Q: Gora works hard  R: Gora gets promotion  S: Gora will be happy The argument can bet written as  (P˄Q)→R  R→S  ¬S ... also be written as: ((P˅Q)˄¬P)→Q where P, and Q are propositions expressed in some formal system.

The language of all non-null strings of a’s can be defined by a context free grammar as follow : S→a S|S a| a The word a3 can be generated by ................ different trees. (A) Two (B) Three (C) Four (D) Five

Description : The language of all non-null strings of a’s can be defined by a context free grammar as follow : S→a S|S a| a The word a3 can be generated by ................ different trees. (A) Two (B) Three (C) Four (D) Five

Last Answer : (C) Four Explanation:

The number of different binary trees with 6 nodes is ............. (A) 6 (B) 42 (C) 132 (D) 256

Description : The number of different binary trees with 6 nodes is ............. (A) 6 (B) 42 (C) 132 (D) 256

Last Answer : (C) 132

The number of different spanning trees in complete graph, K4 and bipartite graph K2,2 have .......... and .....…. respectively. (A) 14, 14 (B) 16, 14 (C) 16, 4 (D) 14, 4

Description : The number of different spanning trees in complete graph, K4 and bipartite graph K2,2 have .......... and .....…. respectively. (A) 14, 14 (B) 16, 14 (C) 16, 4 (D) 14, 4

Last Answer : (C) 16, 4 

Which of the following statement(s) regarding a linker software is/are true? I. A function of a linker is to combine several object modules into a single load module. II. A function of a linker is to replace absolute references in an object module by symbolic references to locations in other modules. (1) Only I (2) Only II (3) Both I and II (4) Neither I nor Il

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A full binary tree with n leaves contains (A) n nodes (B) log2 n nodes (C) 2n –1 nodes (D) 2n nodes

Description : A full binary tree with n leaves contains (A) n nodes (B) log2 n nodes (C) 2n –1 nodes (D) 2n nodes

Last Answer : (C) 2n –1 nodes 

The number of disk pages access in B-tree search, where h is height, n is the number of keys, and t is the minimum degree, is: (A) θ(logn h*t) (B) θ(logt n*h) (C) θ(logh n) (D) θ(logt n)

Description : The number of disk pages access in B-tree search, where h is height, n is the number of keys, and t is the minimum degree, is: (A) θ(logn h*t) (B) θ(logt n*h) (C) θ(logh n) (D) θ(logt n)

Last Answer : Answer: D

The runtime for traversing all the nodes of a binary search tree with n nodes and printing them in an order is (A) O(lg n) (B) O(n lg n) (C) O(n) (D) O(n2 )

Description : The runtime for traversing all the nodes of a binary search tree with n nodes and printing them in an order is (A) O(lg n) (B) O(n lg n) (C) O(n) (D) O(n2 ) 

Last Answer : (C) O(n) 

Any decision tree that sorts n elements has height .............. (1) Ω(log n) (2) Ω(n) (3) Ω(n log n) (4) Ω(n2)

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Last Answer : (3) Ω(n log n) 

MERRY *********, EVERYBODY. I just thought it would be nice to have one thread where we could all leave our best wishes to each other. And I really can’t figure a out a graceful way to end this in question format, OK?

Description : MERRY CHRISTMAS, EVERYBODY. I just thought it would be nice to have one thread where we could all leave our best wishes to each other. And I really can’t figure a out a graceful way to end this in question format, OK?

Last Answer : answer:Twas the night before Xmas and all through the house not a creature was stirring, not even a goose. The pussy cats were draped across the big bed while visions of gophers danced in their heads. And ... away, my electric blanket is heating. ;-D Merry Christmas all, and to all a good night !

Is there a graceful way of giving someone an "out"?

Description : Is there a graceful way of giving someone an "out"?

Last Answer : Simply tell him or her that it’s been taken care of, so that s/he no longer has to. Then, thank the person.

How to make a graceful getaway from a nightmare boss?

Description : How to make a graceful getaway from a nightmare boss?

Last Answer : I don’t think I’d worry too much about burning a bridge that leads to hell. Get another job and move out.

Is there a graceful way to handle someone else's error?

Description : Is there a graceful way to handle someone else's error?

Last Answer : If it was me- I would not finger the secretary or name her- any time you point the finger at someone else it makes you look like you are passing the blame. Instead I would say ... , I am sorry. This way you are taking responsibility while still mentioning that your information was inaccurate.

Graceful is to what as polite is to rude?

Description : Graceful is to what as polite is to rude?

Last Answer : ohhhhhhhh im pro because a+a=2a

If polite is to rude what is to graceful?

Description : If polite is to rude what is to graceful?

Last Answer : Graceful is to clumsy

What is graceful to as polite is to rude?

Description : What is graceful to as polite is to rude?

Last Answer : ohhhhhhhh im pro because a+a=2a